X-semipermutable subgroups of finite groups
By Wenbin Guo, Kar Ping Shum, A. Skiba. 2007
92 citations recorded by the source corpus.
Abstract Let X be a non-empty subset of a group G. Then we call a subgroup A of G a X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T 1 of T there exists an element x ∈ X such that A T 1 x = T 1 x A . In this paper, we study the properties of X-semipermutable subgroups. In particular, a new version of the famous Schur–Zassenhaus Theorem in terms of X-semipermutable subgroups is given.
Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/1cc6f35c1ba32874062afe3ef75caab198b42c1e
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In Artificial Intelligence
In Discrete Mathematics and Combinatorics
In Electrical and Electronic Engineering
Citations in the corpus
- On Some Results in the Theory of Finite Partially Soluble Groups (2016, background): “Observe also that if |G : A| is primary, then obviously the subgroup A G-permutes (in the sense of [22]) with all Sylow subgroups of G.”
- A generalization of a Hall theorem (2016, background): “Then A is said to R-permute with B [5] if for some x ∈ R we have AB = BA.”