6533b824fe1ef96bd127ff3a
RESEARCH PRODUCT
Permutability of injectors with a central socle in a finite solvable group
Rex DarkArnold D. FeldmanMaría Dolores Pérez-ramossubject
Class (set theory)Algebra and Number Theory010102 general mathematicsSylow theoremsPrime numberBasis (universal algebra)01 natural sciencesFitting subgroupSet (abstract data type)CombinatoricsSection (category theory)Solvable group0103 physical sciences010307 mathematical physics0101 mathematicsMathematicsdescription
In response to an Open Question of Doerk and Hawkes [5, IX Section 3, page 615], we shall show that if Zπ is the Fitting class formed by the finite solvable groups whose π-socle is central (where π is a set of prime numbers), then the Zπ-injectors of a finite solvable group G permute with the members of a Sylow basis in G. The proof depends on the properties of certain extraspecial groups [4].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-04-01 | Journal of Algebra |