There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphi...

For partial automorphisms of C∗-algebras, Takai-Takesaki crossed product duality tends to fail, in proportion to the extent to which the partial automorphism is not an automorphism.

The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having 4n+ 6 vertices and automorphism group cyclic of order 4n, n ≥ 1. As a special case we get graphs with 2k + 6 vertices and cyclic automorphism g...

Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X × Y . This implies that the minimal spanning forest corresponding to i.i.d. edge-weights in such a product, has infinitely many connected componen...

This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of Chevalley groups; constructing p-groups with specified automorphism groups; and the discovery of finite p-groups whose automorphism groups are or are not p-groups themselves. The material is presen...

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometri...

If W is a right-angled Coxeter group, then the group Aut(W ) of automorphisms of W acts on the set of conjugacy classes of involutions in W. Following Tits [16], the kernel of this action is denoted by Aut◦(W ). Since W is a CAT(0) group [12], the index of Aut◦(W ) in Aut(W ) is finite and there is a series 1 Inn(W ) Aut◦(W ) Aut(W ) of normal subgroups of Aut(W ). A presentation for Aut◦(W ) w...

If X is a topological space we denote by C(X) ® Mn the algebra of continuous functions from X to the algebra Mn of n x n complex matrices. A complete characterization of those topological spaces Y is given (in terms of vector bundles on Y) such that each unital algebrahomomorphism Φ: C(X) Θ Mn —• C(Y) Mkn is of the form a o (Φ' ® idΛ) for some homomorphism Φ': C(X) -+ C(Y) ® Λ/* and some su...

Let G be a finite p-group, p prime such that G has a normal subgroup H , there exists an element y ∈ G, y / ∈ H such that order of y is p, y ∈ ζ(G) and each element g ∈ G can be written as g = h y, h ∈ H, 1 ≤ i ≤ p, where ζ(G) denotes the center of G. It is proved that any τ ∈ Autc(G) such that for all x ∈ H , xτ = (uy)x(uy), where u is a fixed element of H and 1 ≤ i ≤ p is an inner automorphis...