Let be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley ...

We relate the character theory of symmetric groups S2n and S2n+1 with that hyperoctahedral group Bn=(Z/2)n⋊Sn, as part expectation reductive diagram automorphism their Weyl groups, is related to fixed subgroup automorphism.

We exhibit normal subgroups of a free nilpotent group F of rank two and class three, which have isomorphic finite quotients but are not conjugate under any automorphism of F . A remarkable fact about free profinite groups of finite rank is that any isomorphism between finite quotients of such a group F lifts to an automorphism of F . This is true, more generally, if F a free pro-Cgroup of finit...

In the first paper in this series a structure S was called canonically reconstructible from a structure T provided 5 was canonically isomorphic to a structure T' derived from T. The principle proposition of the paper was the scholium which asserted: If a structure 5 contains a substructure T and if S is canonically reconstructible from T, then every automorphism of T may be extended uniquely to...

In this paper, we will determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this will complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we deter...

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...

In this paper we prove that if two normal affine surfaces $S$ and $S'$ have isomorphic automophism groups, then every connected algebraic group acting regularly faithfully on acts also $S'$. Moreover, is non-toric, show the dynamical type of a 1-torus action preserved in presence an additive action. We complex toric are determined by abstract structure their regular automorphism groups category...

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...