[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 ...
Ballester-Bolinches, A.; Pedraza Aguilera, María Carmen(Cambridge University Press, 2018-02)
[EN] Kang and Liu ['On supersolvability of factorized finite groups', Bull. Math. Sci. 3 (2013), 205-210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is ...
Ballester-Bolinches, A.; Madanha, S. Y.; Mudziiri Shumba, T. M.; Pedraza Aguilera, María Carmen(Cambridge University Press, 2022-04)
[EN] In this paper, we study the structure of finite groups G = AB which are a weakly mutually sn-permutable product of the subgroups A and B, that is, A permutes with every subnormal subgroup of B containing A boolean AND ...
Ballester-Bolinches, A.; Li, Y.; Pedraza Aguilera, María Carmen; Su, Ning(Springer-Verlag, 2020-02-22)
[EN] A subgroup H of a finite group G is called P-subnormal in G if either H = G or it is connected to G by a chain of subgroups of prime indices. In this paper, some structural results of finite groups which are factorised ...
[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 ...
Ballester-Bolinches, A.; Li, Yangming; Pedraza Aguilera, María Carmen; Su, Ning(European Mathematical Society Publishing House, 2018-12-28)
[EN] The main purpose of this paper is to study mutually permutable products G = AB in which the subgroups of prime order p and cyclic of order 4 (if p = 2) of the largest normal subgroup of G contained in A boolean AND B ...
Ballester-Bolinches, A.; Fakieh, W. M.; Pedraza Aguilera, María Carmen(Springer-Verlag, 2019-04)
[EN] In this paper, mutually sn-permutable subgroups of groups belonging to a class of generalised supersoluble groups are studied. Some analogs of known theorems on mutually sn-permutable products are established.
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, A.; Kamornikov, S. F.; Pedraza Aguilera, María Carmen; Pérez-Calabuig, V.(Springer-Verlag, 2020-03-02)
[EN] Let sigma = {sigma(i) : i is an element of I} be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called sigma-subnormal in G if there is a chain of subgroups
X = X-0 subset of X-1 ...