A Characterization of the Finite Groups PSL (n, q).
A condition for the solvability of finite groups.
A note on a class of factorized -groups
In this note we study finite -groups admitting a factorization by an Abelian subgroup and a subgroup . As a consequence of our results we prove that if contains an Abelian subgroup of index then has derived length at most .
A note on a result of Skiba.
A note on factorized (finite) -groups
A note on influence of subgroup restrictions in finite group structure.
Abelian quasinormal subgroups of groups
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
Algorithms for permutability in finite groups
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
-semipermutable subgroups of finite groups.
Caratterizzazione dei gruppi risolubili d'ordine finito complementati
Catene pronormali nei gruppi finiti supersolubili
CLT and non-CLT groups of order
Complements of the socle in almost simple groups
Conditions for p-supersolubility and p-nilpotency of finite soluble groups
Let ℨ be a complete set of Sylow subgroups of a group G. A subgroup H of G is called ℨ-permutably embedded in G if every Sylow subgroup of H is also a Sylow subgroup of some ℨ-permutable subgroup of G. By using this concept, we obtain some new criteria of p-supersolubility and p-nilpotency of a finite group.
Crossed product of cyclic groups
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
Doppelmodulzerlegungen von Gruppen.
Dual-Standard subgroups of finite and locally finite groups.
Endliche Gruppen mit vielen Untergruppen.
Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”
The original version of the article was published in Central European Journal of Mathematics, 2011, 9(4), 915–921, DOI: 10.2478/s11533-011-0029-8. Unfortunately, the original version of this article contains a mistake: Lemma 2.1 (2) is not true. We correct Lemma 2.2 (2) and Theorem 1.1 in our paper where this lemma was used.
Factorization of groups involving symmetric and alternating groups.