Finite p-groups with cyclic center have non-inner automorphisms of order p

IF 0.5 4区 数学 Q3 MATHEMATICS
Mandeep Singh, Mahak Sharma
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引用次数: 0

Abstract

Let p be a prime number. A longstanding conjecture asserts that every finite non-abelian p-group has a non-inner automorphism of order p. In this paper, under some conditions on an odd order finite p-group G with cyclic center, we prove that G exhibits a non-inner automorphism of order p. As a consequence, under certain conditions on a finite p-group G \((p>2),\) the conjecture is proved for all nilpotency classes except class 2 and maximal class. Moreover, we also settle the conjecture for some non-abelian finite 3-groups of coclass 3,  which is a pending case of the main result of Ruscitti et al. (Monatsh. Math. 183(4):679–697, 2016).

具有循环中心的有限p群具有p阶的非内自同构
设p是质数。一个长期猜想证明了每一个有限非阿贝p群都有p阶的非内自同构。本文在具有循环中心的奇阶有限p群G的某些条件下,证明了G具有p阶的非内自同构。因此,在有限p群G的某些条件下\((p>2),\)证明了除了类2和极大类以外的所有幂零类的猜想。此外,我们还解决了一些非阿贝尔有限的共3类3群的猜想,这是Ruscitti et al. (Monatsh)的主要结果的一个待决情况。数学。183(4):679-697,2016)。
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来源期刊
Archiv der Mathematik
Archiv der Mathematik 数学-数学
CiteScore
1.10
自引率
0.00%
发文量
117
审稿时长
4-8 weeks
期刊介绍: Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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