A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids its chief factors. Partial cover and avoidance property has turned out to be very useful ...
[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 ...
[EN] The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent ...
We study finite groups in which every maximal subgroup is
supersoluble or normal. Our results answer some questions arising from
papers of Asaad and Rose.
Ballester Bolinches, Adolfo; Cossey, John; Pedraza Aguilera, María Carmen(Elsevier, 2016-11-16)
In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian ...
[EN] We give some sufficient conditions for a normal p-subgroup P of a finite group G to have every G-chief factor below it cyclic. The S-permutability of some p-subgroups of O^p(G)plays an important role. Some known results ...
[EN] In the paper, a Frattini-like subgroup associated with a class X of simple groups is introduced and analysed. The corresponding X-saturated formations are exactly the X-local ones introduced by Förster. Our techniques ...
[EN] In this paper criteria for a product of formations to be X-local, X a class of simple groups, are obtained. Some classical results on products of saturated formations appear as particular cases.
[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.
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Liriano Castro, Orieta del Corazón de Jesús(Universitat Politècnica de València, 2016-01-07)
[EN] The scope of this thesis is the abstract finite group theory. All the groups we will consider will be finite. hence, the word "group" will be understood as a synonimous of "finite group". We say that a subgroup H of ...
[EN] An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every ...
[EN] In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. As a consequence, new bounds for the number of random generators needed to generate a finite ...
Let Z be a complete set of Sylow subgroups of a finite group G, that is,
a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A
subgroup H of G is called Z-permutable if H permutes with all members ...