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 ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Jiang, Qinhui; Li, Xianhua(SpringerFondazione Annali di Matematica Pura ed Applicata, 2015-02)
In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have ...
[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 ...
Ballester-Bolinches, A; Beidleman, J. C.; Esteban Romero, Ramón; Ragland, M. F.(Cambridge University Press (CUP): STM Journals - No Cambridge Open, 2014-10)
A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the ...
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 ...
[EN] In [J. C. Beidleman, D. J. S. Robinson, J. Algebra 1997, 191, 686--703, Theorem A], Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime ...
[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join <A,B> and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and ...
[EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is ...
[EN] A group G is said to be an involutive Yang¿Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, nondegenerate set-theoretic solution of the Yang-Baxter equation. We give ...
[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also ...
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 ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón(Cambridge University Press, 2003-10)
[EN] Characterisations of finite groups in which normality is a transitive relation are presented
in the paper. We also characterise the finite groups in which every subgroup is either
permutable or coincides with its ...
Esteban Romero, Ramón; Vincenzi, G.(Cambridge University Press (CUP), 2016-04)
We extend to soluble FC∗ -groups, the class of generalised FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes , Serdica Math. J. 28(3) (2002), 241 254], the ...
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 ...
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.
The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose $p$-length is greater than $1$, $p$ a prime number. Alternative ...