We study fixed point properties of the automorphism group universal Coxeter Aut(Wn). In particular, we prove that whenever Aut(Wn) acts by isometries on complete d-dimensional CAT(0) space with d<⌊n2⌋, then it must fix a point. also does not have Kazhdan’s property (T). Further, strong restrictions are obtained homomorphisms to groups do contain copy Sym(n).

configuration, 138Alternating Register Automata, 25Alternating Tree Register Automata,115ancestor relation ( , ≺), 57ARA, 25ARA(guess, spread), 25ARA(guess, spread, <), 32ATRA, 115ATRA(guess, spread), 115attrXPath, 63Aut, 79Aut , 79

We prove that every simplicial automorphism of the free splitting graph of a free group Fn is induced by an outer automorphism of Fn for n ≥ 3. In this note we consider the graph Gn of free splittings of the free group Fn of rank n ≥ 3. Loosely speaking, Gn is the graph whose vertices are non-trivial free splittings of Fn up to conjugacy, and where two vertices are adjacent if they are represen...

S. E. Franks ([email protected]), B. Schwarz, A. Jiménez, R. C. Ydenberg and D. B. Lank, Centre for Wildlife Ecology, Dept of Biological Sciences, Simon Fraser Univ., Burnaby, BC V5A 1S6, Canada. AJ also at: Facultad de Biología, Univ. de La Habana, Havana 10400, Cuba . – D. R. Norris, Dept of Integrative Biology, Univ. of Guelph , Guelph, ON N1G 2W1, Canada. – T. K. Kyser, Queen ’ s Facility for ...

Generic automorphisms are a common theme when one works with auto-morphism groups of countable structures. They play a pivotal role in reconstruction results. In these notes we shall define and explain a notion of generic, due to John Truss, which is highly relevant to reconstruction. The idea is that a generic automorphism acts on the elements of the structure in the least special way, that is...

1 The Setup {s:setup} The starting point is: a group G, a Cartan involution θ, and another involution σ of finite order, commuting with θ. It is natural to consider the coset σK = {σ ◦ int(k) | k ∈ K} ⊂ Aut(G). Every element of this coset commutes with θ. We’re mainly interested when σ is an involution, especially the case σ = θ. Now fix a pinning P = (H,B, {Xα}), and write δ, ǫ ∈ Aut(G) for th...

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...

We investigate the minimality property of the group of homeomor-phisms AUT(C) of some compact set C: In particular we show that for C = 0;1] n the corresponding group is minimal ii n = 1: Also we prove the minimality of AUT(D 1); where D 1 is a Cantor cube with a countable weight. These results partially answer the general question raised by Prodanov and Stojanov ((2]) , Dierolf et.al. ((3]) an...