Groups in which the bounded nilpotency of two-generator subgroups is a transitive relation.
Groups in which the derived groups of all 2-generator subgroups are cyclic
Groups in which the prime graph is a tree
The prime graph of a finite group is defined as follows: the set of vertices is , the set of primes dividing the order of , and two vertices , are joined by an edge (we write ) if and only if there exists an element in of order . We study the groups such that the prime graph is a tree, proving that, in this case, .
Groups of automatic automorphisms of some automatic structures.
Groups of binary relations.
Groups of finite quasi-projective dimension.
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 of Order which is Indivisible by a Fixed Prime
Groups of periods for arbitrary maps on groups.
Groups of piecewise linear homeomorphisms of the real line.
Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
Groups of Prime-Power Order Having an Abelian Centralizer of Type (r, 1).
Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function
We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the -topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.
Groups of simple and multiple antisymmetry of borders.
Groups of simple and multiple antisymmetry of similitude in
Groups of simple and multiple ribbon antisymmetry.
Groups preserving the cardinality of subsets product under permutations
Groups qui reflètent les décompositions de leurs quotients ou de leurs sous-groups
Groups Satisfying the Maximal Condition for Normal Subgroups.
Groups satisfying the maximal condition on subnormal non-normal subgroups
The structure of (generalized) soluble groups for which the set of all subnormal non-normal subgroups satisfies the maximal condition is described, taking as a model the known theory of groups in which normality is a transitive relation.