A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the groups are either: finite, or finite index, virtually free. This result applies, in particular, to systolic groups. prove similar strong restrictions extensions for other classes asymptotically The proof relies stud...

This note investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups for three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups.

This paper studies, for p a prime, rank one isolated -minimal subgroups P in finite group G . Such share many of the features minimal parabolic groups Lie type. The structure Y , normal closure O ( ) is determined where smallest subgroup such that / -group. We find if ? and = 1 then either Z simple type characteristic or ? 7 with given by an explicit list. Of particular note twenty four out six...

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, the nilpotent case. It turns out that context, like for finite nilpotency is equivalent to normalizer property or uniqueness of Sylow subgroups, provided maximal normal torsion-free subgroup nilpotent. As consequence, we show decompositions prove Lie group an expansion reals if...