[EN] In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, ...
A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite ...
[EN] Let p be a prime. The class of all p-soluble groups G such that every p-chief factor of G is cyclic and all p-chief factors of G are G-isomorphic is studied in this paper. Some results on T-, PT-, and
PST -groups are ...
For a finite group G we define the graph $\Gamma(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes $\{\mathcal {A}, \mathcal {B}\}$ are joined by an edge if for ...
A characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding properties enjoyed by all the subgroups is proved in the paper. The key point is an extension ...
[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) ...
Ballester Bolinches, Adolfo; Beidleman, James C.; Esteban Romero, Ramón(Elsevier, 2007-06-01)
[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal ...
We continue here our study of pairwise mutually and pairwise totally permutable
products. We are looking for subgroups of the product in which the given factorization
induces a factorization of the subgroup. In the case ...
[EN] This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G=AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every ...
Ballester-Bolinches, A.; Beidleman, J. C.; Esteban Romero, Ramón; Ragland, M. F.(Elsevier, 2015-05)
[EN] In this survey paper several subgroup embedding properties related to some types of permutability
are introduced and studied.
ª 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University