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On σ -permutably embedded subgroups of finite groups

Chenchen CaoLi ZhangWenbin Guo — 2019

Czechoslovak Mathematical Journal

Let σ = { σ i : i I } be some partition of the set of all primes , G be a finite group and σ ( G ) = { σ i : σ i π ( G ) } . A set of subgroups of G is said to be a complete Hall σ -set of G if every non-identity member of is a Hall σ i -subgroup of G and contains exactly one Hall σ i -subgroup of G for every σ i σ ( G ) . G is said to be σ -full if G possesses a complete Hall σ -set. A subgroup H of G is σ -permutable in G if G possesses a complete Hall σ -set such that H A x = A x H for all A and all x G . A subgroup H of G is σ -permutably embedded in G if H is σ -full...

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