a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

in this article we introduce the notion of n-capable groups. it is shown that every group g admits a uniquely determined subgroup (〖z^n)〗^* (g) which is a characteristic subgroup and lies in the n-centre subgroup of the group g. this is the smallest subgroup of g whose factor group is n-capable. moreover, some properties of n-central extension will be studied.

We present a systematic approach to writing adjoint Higgs vacuum expectation values (vevs), which break a symmetry G to differently embedded isomorphic copies of a subgroup belonging to the chain G ⊃ H1 ⊃ · · · ⊃ Hl, as linear combinations of each other. Given an adjoint Higgs vacuum expectation value h breaking G → H, a full complement of vevs breaking G to different embeddings of the subgroup...

We will give a simplified and a direct proof of a special case of Ratner’s theorem on closures and uniform distribution of individual orbits of unipotent flows; namely, the case of orbits of the diagonally embedded unipotent subgroup acting on SL(2, K)/Γ1 × · · ·×SL(2, K)/Γn, where K is a locally compact field of characteristic 0 and each Γi is a cocompact discrete subgroup of SL(2, K). This sp...

Let Hg be a genus g handlebody and MCG2n(Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg = ∂Hg, fixing a given set of 2n points. In this paper we find a finite set of generators for E 2n, the subgroup of MCG2n(Tg) consisting of the isotopy classes of homeomorphisms of Tg admitting an extension to the handlebody and keeping fixed the union of n disjoint pro...

Previous research has suggested that the local processing bias often reported in studies of Autism Spectrum Condition may only be typical of a subgroup of individuals with autism also presenting with macrocephaly. The current study examined a group of children with autism, with and without macrocephaly, on the Children's Embedded Figures Test (CEFT), a well-established measure of local processi...

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, and whose intersection is a separable subgroup, there are finite index subgrou...

‎let $h$ be a prefrattini subgroup of a soluble finite group $g$‎. ‎in the‎ ‎paper it is proved that there exist elements $x,y in g$ such that the equality‎ ‎$h cap h^x cap h^y = phi (g)$ holds‎.

‎In 1970‎, ‎Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ Atti Accad‎. ‎Naz‎. ‎Lincei Rend‎. ‎Cl‎. ‎Sci‎. ‎Fis‎. ‎Mat‎. ‎Natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $IM$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎A group $G$ is said to have the $FM$...