منابع مشابه
Invariable generation of infinite groups
Article history: Received 30 April 2014 Available online 18 September 2014 Communicated by Charles Leedham-Green
متن کاملInvariable Generation of the Symmetric Group
Abstract. We say that permutations π1, . . . , πr ∈ Sn invariably generate Sn if, no matter how one chooses conjugates π 1 , . . . , π r of these permutations, π 1 , . . . , π r generate Sn. We show that if π1, π2, π3 are chosen randomly from Sn then, with probability tending to 1 as n → ∞, they do not invariably generate Sn. By contrast it was shown recently by Pemantle, Peres and Rivin that f...
متن کاملHigher dimensional Thompson groups
Three groups F ⊆ T ⊆ V , known as Thompson groups, have generated interest since R. J. Thompson introduced them in the late 1960s. Part of their initial interest was the fact that T and V supplied the first known examples of infinite, simple, finitely presented groups. Since then, other properties of the groups have been studied as well as their interaction with other areas of mathematics. The ...
متن کاملAutomorphisms of Generalized Thompson Groups
0.1. Results. We study the automorphisms of some generalizations of Thompson’s groups and their underlying structures. The automorphism groups of two of Thompson’s original groups were analyzed in [2] and were shown to be “small” and “unexotic.” Our results differ sharply from [2] in that we show that the automorphism groups of the generalizations are “large” and have “exotic” elements. The ter...
متن کاملThe homology of the Higman–Thompson groups
We prove that Thompson’s group V is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman–Thompson groups Vn,r with the homology of the zeroth component of the infinite loop space of the mod n− 1 Moore spectrum. As V = V2,1, we can deduce that this group is acyclic. Our proof involves establishing homological stability with respect t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2017.01.019