Real class sizes

2018/03/01 by Hung P. Tong‐Viet, Tong-Viet, Hung P.
Computer Science · Engineering · Mathematics · #20D10 #20E45 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1803.01717

openalex publication_date 2018/03/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the structures of finite groups using some arithmetic conditions on the sizes of real conjugacy classes. We prove that a finite group is solvable if the prime graph on the real class sizes of the group is disconnected. Moreover, we show that if the sizes of all non-central real conjugacy classes of a finite group G have the same 2-part and the Sylow 2-subgroup of G satisfies certain condition, then G is solvable.

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