‎‎in this paper we determine all finite $2$-groups of‎ ‎class $2$ in which every automorphism of order $2$ leaving the frattini subgroup elementwise fixed is inner‎.

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism. This solves the problem 3.9 from [19] for Lie algebras.

We construct some codes, designs and graphs that have the first or second Janko group, J1 or J2, respectively, acting as an automorphism group. We show computationally that the full automorphism group of the design or graph in each case is J1, J2 or J̄2, the extension of J2 by its outer automorphism, and we show that for some of the codes the same is true.

We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism...

A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A#H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A...

Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...

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.

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...