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Invariant class sizes and solvability of finite groups under coprime action
Author(s) -
Beltrán Antonio,
Shao Changguo
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400363
Subject(s) - mathematics , conjugacy class , coprime integers , arithmetic function , automorphism , invariant (physics) , finite group , pure mathematics , combinatorics , discrete mathematics , group (periodic table) , chemistry , organic chemistry , mathematical physics
Suppose that A and G are finite groups of relatively prime orders such that A acts on G via automorphisms, and then, A acts on the set of conjugacy classes of G . We study several arithmetical properties on the sizes of certain classes which are left fixed by A and how they reflect on the A ‐invariant structure and may imply the solvability of G .