In this paper, the unitary dual of p-adic group SO(7) with support on minimal parabolic subgroup is determined. explicit determination external approach used, which represents basic for finding dual, and consists two main steps: a complete description non-unitary extraction classes unitarizable representations among obtained irreducible subquotients. We expect that our results will provide deep...

Let M be a factor with separable predual and G a compact group of automorphisms of M whose action is minimal, i.e. M ′ ∩M = C, where M denotes the G-fixed point subalgebra. Then every intemediate von Neumann algebra M ⊂ N ⊂ M has the form N = M for some closed subgroup H of G. An extension of this result to the case of actions of compact Kac algebras on factors is also presented. No assumptions...

This paper studies type-definable groups in C-minimal structures. We show first for some of these groups, that they contain a cone which is a subgroup. This result will be applied to show that in any geometric locally modular non trivial C-minimal structure, there is a definable infinite C-minimal group.

Let G be a collineation group of a thick finite generalised hexagon or generalised octagon Γ. If G acts primitively on the points of Γ, then a recent result of Bamberg et al. shows that G must be an almost simple group of Lie type. We show that, furthermore, the minimal normal subgroup S of G cannot be a Suzuki group or a Ree group of type G2, and that if S is a Ree group of type F4, then Γ is ...

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...

Consider a cubic extension K := Q(α), when the minimal polynomial f(x) of α does not totally split in K. The normal closure L := (K) is a sextic extension of Q, with Gal(L/Q) = S3. Now we fix notation and pick one embedding of K as K1, say K1 is fixed by (2, 3) ∈ S3. Here (2, 3) has the explicit description that if I choose one root u1 of f(x), (2, 3) permute the other two conjugate roots of u1...

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal “infinitesimal subgroup” G such that the quotient G/G, equipped with the “logic topology”, is a compact (real) Lie group. Our first result is that the functor G 7→ G/G sends exact sequences of definably compact groups into exacts sequences of Lie group...