6533b86cfe1ef96bd12c7f56
RESEARCH PRODUCT
On a paper of Beltrán and Shao about coprime action
H. MengH. MengAdolfo Ballester-bolinchesAdolfo Ballester-bolinchessubject
Algebra and Number TheoryCoprime integersMathematics::Number Theory010102 general mathematicsStructure (category theory)Automorphism01 natural sciencesPrime (order theory)Action (physics)CombinatoricsMathematics::Group Theory0103 physical sciences010307 mathematical physics0101 mathematicsMathematicsdescription
Abstract Assume that A and G are finite groups of coprime orders such that A acts on G via automorphisms. Let p be a prime. The following coprime action version of a well-known theorem of Ito about the structure of a minimal non-p-nilpotent groups is proved: if every maximal A-invariant subgroup of G is p-nilpotent, then G is p-soluble. If, moreover, G is not p-nilpotent, then G must be soluble. Some earlier results about coprime action are consequences of this theorem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-08-01 | Journal of Pure and Applied Algebra |