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Groups containing locally maximal product-free sets of size 4 包含大小为4的局部最大无乘积集的群
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-07-19 DOI: 10.12958/ADM1347
C. Anabanti
{"title":"Groups containing locally maximal product-free sets of size 4","authors":"C. Anabanti","doi":"10.12958/ADM1347","DOIUrl":"https://doi.org/10.12958/ADM1347","url":null,"abstract":"Every locally maximal product-free set S in a finite group G satisfies G=S∪SS∪S−1S∪SS−1∪S−−√, where SS={xy∣x,y∈S}, S−1S={x−1y∣x,y∈S}, SS−1={xy−1∣x,y∈S} and S−−√={x∈G∣x2∈S}. To better understand locally maximal product-free sets, Bertram asked whether every locally maximal product-free set S in a finite abelian group satisfy |S−−√|≤2|S|. This question was recently answered in the negation by the current author. Here, we improve some results on the structures and sizes of finite groups in terms of their locally maximal product-free sets. A consequence of our results is the classification of abelian groups that contain locally maximal product-free sets of size 4, continuing the work of Street, Whitehead, Giudici and Hart on the classification of groups containing locally maximal product-free sets of small sizes. We also obtain partial results on arbitrary groups containing locally maximal product-free sets of size 4, and conclude with a conjecture on the size 4 problem as well as an open problem on the general case.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42697530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A new characterization of projective special linear groups L3(q) 射影特殊线性群L3（q）的一个新刻画
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-07-19 DOI: 10.12958/ADM1235
B. Ebrahimzadeh
{"title":"A new characterization of projective special linear groups L3(q)","authors":"B. Ebrahimzadeh","doi":"10.12958/ADM1235","DOIUrl":"https://doi.org/10.12958/ADM1235","url":null,"abstract":"In this paper, we prove that projective special linear groups L3(q), where 0<q=5k±2 (k∈Z) and q2+q+1 is a~prime number can be uniquely determined by their order and the number of elements with same order.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47435345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semisymmetric Zp-covers of the C20 graph C20图的半对称Zp覆盖
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-07-19 DOI: 10.12958/ADM252
A. Talebi, N. Mehdipoor
{"title":"Semisymmetric Zp-covers of the C20 graph","authors":"A. Talebi, N. Mehdipoor","doi":"10.12958/ADM252","DOIUrl":"https://doi.org/10.12958/ADM252","url":null,"abstract":"A graph X is said to be G-semisymmetric if it is regular and there exists a subgroup G of A:=Aut(X) acting transitively on its edge set but not on its vertex set. In the case of G=A, we call X a semisymmetric graph. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields. In this study, by applying concept linear algebra, we classify the connected semisymmetric zp-covers of the C20 graph.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41354598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Constructions of BiHom-X algebras and bimodules of some BiHom-dialgebras bihm - x代数的构造及若干bihm -对偶代数的双模
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-05-05 DOI: 10.12958/adm2023
I. Laraiedh, S. Silvestrov
{"title":"Constructions of BiHom-X algebras and bimodules of some BiHom-dialgebras","authors":"I. Laraiedh, S. Silvestrov","doi":"10.12958/adm2023","DOIUrl":"https://doi.org/10.12958/adm2023","url":null,"abstract":"The aim of this paper is to introduce and to develop several methods for constructions of BiHom-X algebras by extending composition methods, and by using Rota-Baxter operators and some elements of centroids. The bimodules of BiHom-left symmetric dialgebras, BiHom-associative dialgebras and BiHom-tridendriform algebra are defined, and it is shown that a sequence of this kind of bimodules can be constructed. Their matched pairs of BiHom-left symmetric, BiHom-associative dialgebras BiHom-tridendriform algebra are introduced and methods for their constructions and properties are investigated.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48244403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Morita equivalence of semirings with local units 具有局部单元的半环的Morita等价
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-04-10 DOI: 10.12958/ADM1288
Monali Das, Sugato Gupta, S. Sardar
{"title":"Morita equivalence of semirings with local units","authors":"Monali Das, Sugato Gupta, S. Sardar","doi":"10.12958/ADM1288","DOIUrl":"https://doi.org/10.12958/ADM1288","url":null,"abstract":"In this paper we study some necessary and sufficient conditions for two semirings with local units to be Morita equivalent. Then we obtain some properties which remain invariant under Morita equivalence.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44234366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On extension of classical Baer results to Poisson algebras 经典Baer结果在泊松代数中的推广
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-04-10 DOI: 10.12958/ADM1758
L. A. Kurdachenko, A. A. Pypka, I. Subbotin
{"title":"On extension of classical Baer results to Poisson algebras","authors":"L. A. Kurdachenko, A. A. Pypka, I. Subbotin","doi":"10.12958/ADM1758","DOIUrl":"https://doi.org/10.12958/ADM1758","url":null,"abstract":"In this paper we prove that if P is a Poisson algebra and the n-th hypercenter (center) of P has a finite codimension, then P includes a finite-dimensional ideal K such that P/K is nilpotent (abelian). As a corollary, we show that if the nth hypercenter of a Poisson algebra P (over some specific field) has a finite codimension and P does not contain zero divisors, then P is an abelian algebra.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44670539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structure of relatively free trioids 相对自由三元体的结构
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-04-10 DOI: 10.12958/ADM1732
A. Zhuchok
{"title":"Structure of relatively free trioids","authors":"A. Zhuchok","doi":"10.12958/ADM1732","DOIUrl":"https://doi.org/10.12958/ADM1732","url":null,"abstract":"Loday and Ronco introduced the notions of a~trioid and a trialgebra, and constructed the free trioid of rank 1 and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free trialgebra and the free trioid, the free commutative trioid, the free n-nilpotent trioid, the free left (right) n-trinilpotent trioid, and the free rectangular trioid. Some of these results can be applied to constructing relatively free trialgebras.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45792003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the structure of some groups having finite contranormal subgroups 关于具有有限次群的群的结构
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/ADM1724
L. A. Kurdachenko, N. N. Semko
{"title":"On the structure of some groups having finite contranormal subgroups","authors":"L. A. Kurdachenko, N. N. Semko","doi":"10.12958/ADM1724","DOIUrl":"https://doi.org/10.12958/ADM1724","url":null,"abstract":"Following J.S. Rose, a subgroup H of the group G is said to be contranormal in G, if G=HG. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent groups having a finite proper contranormal p-subgroup.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The prime spectrum of the universal enveloping algebra of the 1-spatial ageing algebra and of U(gl2) 1-空间老化代数和U(gl2)的泛包络代数的素谱
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/ADM1761
V. Bavula, T. Lu
{"title":"The prime spectrum of the universal enveloping algebra of the 1-spatial ageing algebra and of U(gl2)","authors":"V. Bavula, T. Lu","doi":"10.12958/ADM1761","DOIUrl":"https://doi.org/10.12958/ADM1761","url":null,"abstract":"For the algebras in the title, their prime, primitive and maximal spectra are explicitly described. For each prime ideal an explicit set of generators is given. An explicit description of all the containments between primes is obtained.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66419858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some commutativity criteria for 3-prime near-rings 3素数近环的交换性判定
IF 0.2
Algebra & Discrete Mathematics Pub Date : 2021-01-01 DOI: 10.12958/adm1439
A. Raji
{"title":"Some commutativity criteria for 3-prime near-rings","authors":"A. Raji","doi":"10.12958/adm1439","DOIUrl":"https://doi.org/10.12958/adm1439","url":null,"abstract":"In the present paper, we introduce the notion of∗-generalized derivation in near-ring N and investigate some properties in volving that of∗-generalized derivation of a∗-prime near-ring N which forces N to be a commutative ring. Some properties of generalized semiderivations have also been given in the context of 3-prime near-rings. Consequently, some well known results have beengeneralized. Furthermore, we will give examples to demonstratethat the restrictions imposed on the hypothesis of various resultsare not superŕuous.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66417619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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