Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

A path integral description of an effective action of monopoles in Abelian projections of Yang-Mills theories is discussed and used to establish a projection independence of the effective action. A dynamic regime in which the effective dynamics may contain massive solitonic excitations is described. Numerical simulations of lattice Yang-Mills theories show that certain topological defects, whic...

The aim of this note is to introduce the latest results of research on the homotopy equivalence of a subgroup complex. Let P be a poset(= partially ordered set). The order complex of P is denoted by the symbol ∆(P ); this is the simplicial complex whose k-dimensional simplices are the non-empty chains x0 < x1 < · · · < xk of P . For a finite group G and a prime number p dividing its order, the ...

We show that amalgams of nitely generated torsionfree nilpotent groups of class c along a cyclic subgroup satisfy a polynomial isoperimetric inequality of degree 4c. The distortion of the amalgamated subgroup is bounded above by a polynomial of degree c. We also give an example of a non-cyclic amalgam of nitely generated torsionfree nilpotent groups along an abelian, isolated and normal subgrou...

Abstract The structure of locally soluble periodic groups in which every abelian subgroup is cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with non-periodic case. also describe finite all subgroups are cyclic.

Given a toric affine algebraic variety $X$ and collection of one-parameter unipotent subgroups $U_1,\ldots,U_s$ $\mathop{\rm Aut}(X)$ which are normalized by the torus acting on $X$, we show that group $G$ generated verifies following alternative Tits' type: either is group, or it contains non-abelian free subgroup. We deduce if $2$-transitive $G$-orbit in then subgroup, so, exponential growth.

We prove that for any prime number p, every finite non-abelian p-group G of class 2 has a noninner automorphism of order p leaving either the Frattini subgroup Φ(G) or Ω1(Z(G)) elementwise fixed.

We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer. supported by DFG grant GRK 209/3-98

Suppose that G is a compact Abelian group. If A ⊂ G then how small can ‖χA‖A(G) be? In general there is no non-trivial lower bound. In [5] Green and Konyagin showed that if Ĝ has sparse small subgroup structure and A has density α with α(1−α) ≫ 1 then ‖χA‖A(G) does admit a non-trivial lower bound. To complement this [11] addressed the case where Ĝ has rich small subgroup structure and further c...