Invariant class sizes and solvability of finite groups under coprime action | Zendy

Beltrán Antonio | Zendy; Shao Changguo | Zendy

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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 .

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