PSLn(9) 群共轭旋转的生成集

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-08-14 DOI:10.1007/s10469-024-09748-z

R. I. Gvozdev

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引用次数: 0

摘要

G.马勒、J.萨克斯尔和 T.魏格尔在[Geom. Ded., 49, No. 1, 85-116 (1994)]中提出了如下问题：对于每个有限简单非阿贝尔群 G，求乘积等于 1 的共轭渐开线的生成数 nc(G) 的最小值。The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (Eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf] 中的问题 14.69c)。J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] 解决了奇数阶 q 域上的零星、交替和投影特殊线性群 PSLn(q) 的这个问题，除了 n ≥ 4 的 q = 9 和 n = 6 的 q ≡ 3 (mod 4) 两种情况。

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Generating Sets of Conjugate Involutions of Groups PSLn(9)

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Generating Sets of Conjugate Involutions of Groups PSLn(9)

G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., 49, No. 1, 85-116 (1994)] formulated the following problem: For every finite simple non-Abelian group G, find the minimum number n_c(G) of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (Eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf].) J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] solved this problem for sporadic, alternating, and projective special linear groups PSL_n(q) over a field of odd order q, except in the case q = 9 for n ≥ 4 and also in the case q ≡ 3 (mod 4) for n = 6. Here we lift the restriction q ≠ 9 for dimensions n ≥ 9 and n = 6.

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.