Related papers: What is the monster?
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
We define the notion of a (linearly reductive) center for a linearly reductive quantum group, and show that the quotient of a such a quantum group by its center is simple whenever its fusion semiring is free in the sense of Banica and…
We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced $C^\ast$-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided.…
We characterize $C^*$-simplicity for countable groups by means of the following dichotomy. If a group is $C^*$-simple, then the action on the Poisson boundary is essentially free for a generic measure on the group. If a group is not…
It is known that in any free group the isolator of finitely generated subgroup is finitely generated subgroup. A very simple proof of this statement is proposed.
In this paper we give a complete algebraic description of groups elementarily equivalent to a given free nilpotent group of finite rank.
We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer…
Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer groups Fi22, the Baby Monster B and the Monster M, is a group algebra.
We construct words with small image in a given finite alternating or unimodular group. This shows that word width in these groups is unbounded in general.
The object of this paper is to examine finite solvable groups whose integral group rings have only trivial central units.
Presenting a finite group by a free product of finite cyclic groups the Hopf formula for the Schur multiplier affords also a covering group, and this has minimal exponent provided that the order of the generators is preserved. This…
We study inert and compressed subgroups of free groups and provide a generalization of echelon subgroups.
We provide an elementary proof that subgroups of free groups are free via group actions.
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of…
A free Steiner quasigroup is a free object in the variety of Steiner quasigroups. Free Steiner quasigroups are characterised by the existence of a levelled construction that starts with a free base - that is, a set of elements none of which…
This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…
A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary…
The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…
This note aims to introduce a left adjoint functor to the functor which assigns a heap to a group. The adjunction is monadic. It is explained how one can decompose a free group functor through the previously introduced adjoint and employ it…