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 of automatic automorphisms of some automatic structures.
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 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 preserving the cardinality of subsets product under permutations
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.
Groups saturated by a finite set of groups.
Groups which are isomorphic to their nonabelian subgroups
Groups whose all subgroups are ascendant or self-normalizing
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972,...
Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)
Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.
Groups whose proper subgroups are locally finite-by-nilpotent
If is a class of groups, then a group is said to be minimal non -group if all its proper subgroups are in the class , but itself is not an -group. The main result of this note is that if is an integer and if is a minimal non (respectively, )-group, then is a finitely generated perfect group which has no non-trivial finite factor and such that is an infinite simple group; where (respectively, , ) denotes the class of nilpotent (respectively, nilpotent of class at most , locally...
Groups with all subgroups permutable or of finite rank
In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.
Groups with all subgroups subnormal or nilpotent-by-Chernikov