The invariably generating graph of the alternating and symmetric groups

Author:

Garzoni Daniele1

Affiliation:

1. Dipartimento di Matematica “Tullio Levi-Civita” , Università degli Studi di Padova , Padova , Italy

Abstract

Abstract Given a finite group G, the invariably generating graph of G is defined as the undirected graph in which the vertices are the nontrivial conjugacy classes of G, and two classes are adjacent if and only if they invariably generate G. In this paper, we study this object for alternating and symmetric groups. The main result of the paper states that if we remove the isolated vertices from the graph, the resulting graph is connected and has diameter at most 6.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference16 articles.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the probability of generating invariably a finite simple group;Journal of Pure and Applied Algebra;2023-06

2. CONNECTED COMPONENTS IN THE INVARIABLY GENERATING GRAPH OF A FINITE GROUP;Bulletin of the Australian Mathematical Society;2021-03-25

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