Extensions realising a faithful abstract kernel and their automorphisms.
FC-nilpotent products of hypercentral groups.
Finiteness of a non-abelian tensor product of groups.
Frattini normal subgroups of finite groups.
Free products with amalgamation of finite groups and finite outer automorphism groups of free groups
Free pro-p groups with operators.
Generalized orbifold Euler characteristic of symmetric products and equivariant Morava -theory.
Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces.
Generating numbers for wreath products
Generating wreath products and their augmentation ideals
Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs
Group extensions and automorphism group rings.
Group Extensions and Splitting Modules.
Group extensions, crossed pairs and an eight term exact sequence.
Group Extensions with Infinite Conjugacy Classes
We characterize the group property of being with infinite conjugacy classes (or icc, i.e. infinite and of which all conjugacy classes except are infinite) for groups which are extensions of groups. We prove a general result for extensions of groups, then deduce characterizations in semi-direct products, wreath products, finite extensions, among others examples we also deduce a characterization for amalgamated products and HNN extensions. The icc property is correlated to the Theory of von Neumann...
Groupes with free 2-generator subsemigroups.
Groups of given intermediate word growth
We show that there exists a finitely generated group of growth for all functions satisfying for all large enough and the positive root of . Set ; then all functions that grow uniformly faster than are realizable as the growth of a group.We also give a family of sum-contracting branched groups of growth for a dense set of .
Groups with Decomposable Set of Quasinormal Subgroups
A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.
Groups with every subgroup ascendant-by-finite
A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
Groups with Normalizer Condition.