For a group G with G-conjugacy class of involutions X, the local fusion graph F(G,X) has X as its vertex set, with distinct vertices x and y joined by an edge if, and only if, the product xy has odd order. Here we show that, with only three possible exceptions, for all pairs (G,X) with G a sporadic simple group or the automorphism group of a sporadic simple group, F(G,X) has diameter 2.

In this paper, we study a relative two-weight Z2Z4-additive codes. It is shown that the Gray image of a two-distance Z2Z4-additive code is a binary two-distance code and that the Gray image of a relative two-weight Z2Z4-additive code, with nontrivial binary part, is a linear binary relative two-weight code. The structure of relative two-weight Z2Z4-additive codes are described. Finally, we disc...

Let X be an infinite-dimensional separable real or complex Banach space and A a closed standard operator algebra on X. Then every local automorphism of A is an automorphism. The assumptions of infinitedimensionality, separability, and closeness are all indispensable.

We determine the n−automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.

These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets. Keywords—Automorphism groups of graphs; Cayley graphs; transposition sets.

In mathematics, automorphisms of algebraic structures play an important role. Automorphisms capture the symmetries inherent in the structures and many important results have been proved by analyzing the automorphism group of the structure. For example, Galois characterized degree five univariate polynomials f over rationals whose roots can be expressed using radicals (using addition, subtractio...

Let Fn be a free group of rank n. An automorphism of Fn is called an IA-automorphism if it trivially acts on the abelianization H of Fn. We denote by IAn the group of IA-automorphisms and call it the IA-automorphism group of Fn. For any integer d ≥ 2, let IAn,d be the group of automorphisms of Fn which trivially acts on H⊗ZZ/dZ. We call IAn,d the congruence IA-automorphism group of Fn of level ...