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...

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...

Suppose that N is a normal subgroup of G with d(G/N) ≤ d and choose g1, . . . , gd such thatG = 〈g1, . . . , gd, N〉. It was noticed by Gaschütz [10] that the cardinality of the set Ωg1,...,gd = {(n1, . . . , nd) ∈ Nd | 〈g1n1, . . . , gdnd〉 = G} is independent on the choice of g1, . . . , gd; namely |Ωg1,...,gd | = φG(d) φG/N (d) . Let PG,N (d) = PG(d) PG/N (d) = φG(d) φG/N (d)|N |d ; this numbe...

The goal of this paper is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a...

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.

We prove that for “most” closed 3-dimensional manifolds M, the existence of a non singular one-form in given cohomology class u∈H 1 (M,ℝ)=Hom(π (M),ℝ) is equivalent to fact every twisted Alexander polynomial Δ H (M,u)∈ℤ[G/keru] associated normal subgroup with finite index H<π (M) has unitary u-minimal term.

In this paper we continue the study of intuitionistic fuzzy groups by introducing the notion of intuitionistic fuzzy normal subgroup based on intuitionistic fuzzy space as a generalization of fuzzy normal subgroup. MSC2000 : 20N25, 03E72. Key Word : Fuzzy space, intuitionistic fuzzy space, intuitionistic fuzzy group, normal intuitionistic fuzzy subgroup .

The goal of this survey is to study some classes of groups determined by different types of complementation of their normal subgroup lattices. The groups whose normal subgroup lattices are Stone lattices, boolean lattices or ortholattices will be also investigated. MSC (2000): Primary 20D30, Secondary 20E15, 06C15, 06D15.