35 research outputs found
Corrigendum to “Sets of elements that pairwise generate a linear group” [J. Combin. Theory Ser. A 115 (3) (2008) 442–465]
The character table of a split extension of the Heisenberg group by , odd
In this paper we determine the full character table of a certain split
extension of the Heisenberg group by the
odd-characteristic symplectic group .Comment: 9 page
On intermediate subfactors of Goodman-de la Harpe-Jones subfactors
In this paper we present a conjecture on intermediate subfactors which is a
generalization of Wall's conjecture from the theory of finite groups. Motivated
by this conjecture, we determine all intermediate subfactors of
Goodman-Harpe-Jones subfactors, and as a result we verify that
Goodman-Harpe-Jones subfactors verify our conjecture. Our result also gives a
negative answer to a question motivated by a conjecture of
Aschbacher-Guralnick.Comment: To appear in Comm. Math. Phy
Expansion in perfect groups
Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an
integer q, denote by Ga_q the subgroup of Ga consisting of the elements that
project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q
with respect to the generating set S form a family of expanders when q ranges
over square-free integers with large prime divisors if and only if the
connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas
are explained in more details in the introduction, typos corrected, results
and proofs unchange
Generators and commutators in finite groups; abstract quotients of compact groups
Let N be a normal subgroup of a finite group G. We prove that under certain
(unavoidable) conditions the subgroup [N,G] is a product of commutators [N,y]
(with prescribed values of y from a given set Y) of length bounded by a
function of d(G) and |Y| only. This has several applications: 1. A new proof
that G^n is closed (and hence open) in any finitely generated profinite group
G. 2. A finitely generated abstract quotient of a compact Hausdorff group must
be finite. 3. Let G be a topologically finitely generated compact Hausdorff
group. Then G has a countably infinite abstract quotient if and only if G has
an infinite virtually abelian continuous quotient.Comment: This paper supersedes the preprint arXiv:0901.0244v2 by the first
author and answers the questions raised there. Latest version corrects
erroneous Lemma 4.30 and adds new Cor. 1.1