Constituents of the product of characters in odd order groups.
Construction of finite soluble groups. (Konstruktion endlicher auflösbarer Gruppen.)
Die dritte Loewy Schicht von P1.
Ein allgemeiner Sylowsatz in endlichen auflösbaren Gruppen.
Einige Sätze über Deck-Meide-Untergruppen endlicher auflösbarer Gruppen.
Elementary Abelian operator groups.
Endliche Gruppen mit Untergruppen mit paarweise teilerfremden Indizes.
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
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.
Exact covering systems for groups
Existencia de inyectores en grupos finitos respecto de ciertas clases de Fitting.
In this paper we prove that all finite groups have F-injectors with respect to a saturated and extensible Fitting formation F.
Factorizations of one-generated -local formations.
Finite Groups Generated by 3-Transpositions. I.
Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup
Let be a finite group. We prove that if every self-centralizing subgroup of is nilpotent or subnormal or a TI-subgroup, then every subgroup of is nilpotent or subnormal. Moreover, has either a normal Sylow -subgroup or a normal -complement for each prime divisor of .
Finite groups in which every two elements generate a soluble subgroup.
Finite groups in which subnormalizers are subgroups
Finite groups in which Sylow normalizers have nilpotent Hall supplements.
Finite groups in which -quasinormality is a transitive relation
Finite groups whose all proper subgroups are -groups
A group is said to be a -group if for every divisor of the order of , there exists a subgroup of of order such that is normal or abnormal in . We give a complete classification of those groups which are not -groups but all of whose proper subgroups are -groups.
Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements
Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups whose set of numbers of subgroups of possible orders has exactly two elements. We show that if is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then has a normal Sylow subgroup of prime order and is solvable. Moreover, as an application we give a detailed description of non-nilpotent groups with...