Magnetic monopole solutions naturally arise in the context of spontaneously broken gauge theories. When the unbroken symmetry includes a non-Abelian subgroup, investigation of the low-energy monopole dynamics by means of the moduli space approximation reveals degrees of freedom that can be attributed to massless monopoles. These do not correspond to distinct solitons, but instead are manifested...

Abstract I review some aspects of BPS magnetic monopoles and of electric-magnetic duality in theories with arbitrary gauge groups. When the symmetry is maximally broken to a U(1)r subgroup, all magnetically charged configurations can be understood in terms of r species of massive fundamental monopoles. When the unbroken group has a non-Abelian factor, some of these fundamental monopoles become ...

The present article is a summary of joint work of the author and Phillip Wesolek on the normal subgroup structure of totally disconnected locally compact second-countable (t.d.l.c.s.c.) groups. The general strategy is as follows: We obtain normal series for a t.d.l.c.s.c. group in which each factor is ‘small’ or a non-abelian chief factor; we show that up to a certain equivalence relation (call...

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....

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 [3] Green and Konyagin show 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. In this paper we address, by contrast, groups with duals having rich small subgroup structure, spe...

‎for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$‎. ‎the aim of this paper is to classify all the non-nilpotent groups with $nu(g)=3$‎.

It is shown that the super Higgs mechanism that occurs in a wide class of models with vanishing cosmological constant (at the classical level) is obtained by the gauging of a flat group which must be an electric subgroup of the duality group. If the residual massive gravitinos which occur in the partial supersymmetry breaking are BPS saturated, then the flat group is non abelian. This is so for...

Abelian subgroups play a key role in the theory and applications of finite p-groups. Our purpose is to establish some very general results motivated by special results that have been of use. In particular, it is known [KJ] that if a finite p-group, for odd p, has an elementary abelian subgroup of order p, n ≤ 5, then it has a normal elementary abelian subgroup of the same order. Our first main ...

Using graph-theoretic techniques for f.g. subgroups of F we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. Also we obtain an analogue of Greenberg-Stallings Theorem for f.g. fully residually free groups, and prove that a f.g. non-abelian subgroup of a f.g. fully residually fre...