Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2021-03-26 , DOI: 10.1142/s0219498822501286 Dan Levy 1
Kayal and Nezhmetdinov introduced in [Factoring groups efficiently, Int. Colloquium on Automata Languages and Programming (Springer, Berlin, Heidelberg, 2009), pp. 585–596] the concept of an irreducible conjugacy class and defined, for any finite non-abelian group, a simple graph on the set of all such classes. This graph is a key ingredient in their proposed algorithm for solving the group decomposition problem. This paper considers the class of finite groups for which the KN-graph is complete (KN-complete groups). The main result is a necessary and sufficient condition for a given group to be KN-complete, formulated in terms of its minimal non-central normal subgroups. This condition is used to obtain a more detailed description of the rather rich class of KN-complete groups.
中文翻译:
关于 KN 完备群的类
Kayal 和 Nezhmetdinov 在 [Factoring groups Effectively, Int.] 中介绍。自动机座谈会语言和 Programming (Springer, Berlin, Heidelberg, 2009), pp. 585–596] 不可约共轭类的概念,并为任何有限非阿贝尔群定义了所有此类类的集合上的简单图。该图是他们提出的用于解决组分解问题的算法的关键要素。本文考虑了 KN 图完备的有限群类(KN-完备群)。主要结果是给定组是 KN 完全的必要和充分条件,根据其最小非中心正态子组表示。该条件用于获得对相当丰富的 KN 完全群类的更详细描述。