groups with the same number of centralizers

2019/06/22 by Khoramshahi, K., Zarrin, M. · 1 citation
#D20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1906.09424

Abstract

For any group G, let nacent(G) denote the set of all nonabelian centralizers of G. Amiri and Rostami in (Publ. Math. Debrecen 87/3-4 (2015), 429-437) put forward the following question: Let H and G be finite simple groups. Is it true that if |nacent(H)| = |nacent(G)|, then G is isomorphic to H? In this paper, among other things, we give a negative answer to this question.

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