7 Davis, J.A., Construction of relative difference sets in p-groups, Discrete Mathematics 103 (1992) 7-15. Jungnickel (1982) and Elliot and Butson (1966) have shown that (pi+ , p, pi+•, pi) relative difference sets exist in the elementary abelian p-group case (p an odd prime) and many 2-groups for the case p = 2. This paper provides two new constructions of relative difference sets with these p...

We consider amalgamations of nitely generated nilpotent groups of class c. We show that doubles satisfy a polynomial isoperimetric inequality of degree 2c. Generalising doubles we introduce non-twisted amalgamations and show that they satisfy a polynomial isoperimetric inequality as well. We give a su cient condition for amalgamations along abelian subgroups to be non-twisted and thereby to sat...

This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup the general skew linear group $\GL_n(D)$ over a division ring $D$. It turns out that in case where $D$ is non-commutative, if such exist, then either it abelian or $[D:F]<\infty$. Also, $F$ infinite field $n\geq 5$, every normal $\GL_n(F)$ abelian.

We present deterministic algorithms for the Hidden Subgroup Problem. The first algorithm, abelian groups, achieves same asymptotic worst-case query complexity as optimal randomized namely~$ \Order(\sqrt{ n}\, )$, where~$n$ is order of group. analogous algorithm non-abelian groups comes within a~$\sqrt{ \log n}$ factor complexity. best known Problem has \emph{expected\/} that sensitive to input,...

Abstract In [16], Peterzil and Steinhorn proved that if a group G definable in an o -minimal structure is not definably compact, then contains torsion-free subgroup of dimension 1. We prove here p -adic analogue the Peterzil–Steinhorn theorem, special case abelian groups. Let be -adically closed field M . If compact there H 1 which compact. future paper we will generalize this to non-abelian

Let G1 × G2 be a subgroup of SO3(R) such that the two factors G1 and G2 are non-trivial groups. We show that if G1 × G2 is not abelian, then one factor is the (abelian) group of order 2, and the other factor is nonabelian and contains an element of order 2. There exist finite and infinite such non-abelian subgroups. Let F2 be the free group of rank 2. It is well-known that the group SO3(R) has ...

A general study of non-abelian duality is presented. We first identify a possible obstruction to the conformal invariance of the dual theory for non-semisimple groups. We construct the exact non-abelian dual for any Wess-Zumino-Witten (WZW) model for any anomaly free subgroup, and the corresponding extension for coset conformal field theories. We characterize the exact non-abelian dual for σ-mo...

a group is called morphic if for each normal endomorphism α in end(g),there exists β such that ker(α)= gβ and gα= ker(β). in this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= gβ and gα = ker(γ). we call g quasi-morphic, if this happens for any normal endomorphism α in end(g). we get the following results: g is quasi-morphic if and only if, for any ...

‎In this study‎, ‎Frattini supplement subgroup and Frattini supplemented group‎ ‎are defined by Frattini subgroup‎. ‎By these definitions‎, ‎it's shown that‎ ‎finite abelian groups are Frattini supplemented and every conjugate of a‎ ‎Frattini supplement of a subgroup is also a Frattini supplement‎. ‎A group action‎ ‎of a group is defined over the set of Frattini supplements of a normal‎ ‎subgro...

In this paper, we will consider finitely presented groups that have a finite index subgroup which admits a surjective homomorphism onto a non-abelian free group. Gromov called these groups large [4]. Large groups have particularly nice properties (for example, super-exponential subgroup growth). They also play an important rôle in lowdimensional topology: it is a major conjecture that the funda...