Introduction. The inner automorphism of an element g of a group G is denoted by ig and is given by the formula xig = gxg−1 for all x ∈ G. The mapping π : G→Aut(G), taking each g∈G to the inner automorphism ig, is a homomorphism, Ker(π) = Z(G) and Im(π) = Inn(G). It is easy to check that the automorphism group Aut(G) of a group G with trivial center also is a group with trivial center. Therefore...

Let M be an ℵ 0 -categorical structure and assume that has no algebraicity weak elimination of imaginaries. Generalizing classical theorems de Finetti Ryll-Nardzewski, we show any ergodic, Aut(M)-invariant measure on [0,1] is a product measure. We also investigate the action Aut(M) compact space LO(M) linear orders M. If moreover Aut(M)↷M transitive, prove Aut(M)↷LO(M) either fixed point or uni...

Extreme demand avoidance (EDA) is increasingly described as part of the autism spectrum and sometimes diagnosed Pathological Demand Avoidance (PDA). Yet little known, about educational experiences children with without EDA behaviours. Using an online survey collecting both quantitative qualitative data, 211 parents reported on school their autistic children. 57 had a child additional diagnosis ...

We show that an action of SL(2, p), p ≥ 7 an odd prime such that 4 6 | (p − 1), has exactly two orbital digraphs Γ1, Γ2, such that Aut(Γi) admits a complete block system B of p + 1 blocks of size 2, i = 1, 2, with the following properties: the action of Aut(Γi) on the blocks of B is nonsolvable, doubly-transitive, but not a symmetric group, and the subgroup of Aut(Γi) that fixes each block of B...

If L is a lattice, the automorphism group of L is denoted Aut(L). It is known that given a finite abstract group H, there exists a finite distributive lattice D such that Aut(D) £= H. It is also known that one cannot expect to find a finite orthocomplemented distributive (Boolean) lattice B such that Aut(B) s= H. In this paper it is shown that there does exist a finite orthomodular lattice L su...

Abstract. Let C be an extremal self-dual binary code of length 72 and g ∈ Aut(C) be an automorphism of order 2. We show that C is a free F2〈g〉 module and use this to exclude certain subgroups of order 8 of Aut(C). We also show that Aut(C) does not contain an element of order 10. Combining these results with the ones obtained in earlier papers we find that the order of Aut(C) is either 5 or divi...

is its closed normal subgroup, [Sh], [Ka]. The group Aut∗k k [n] is an infinite dimensional simple algebraic group, [Sh]. If D is a locally nilpotent k-derivation of k, then it is easily seen that exp tD ∈ Aut∗k k [n] for any t ∈ k, so D lies in Lie(Aut∗k k ). It follows from [BB1], [BB2] that n − 1 is the maximum of dimensions of algebraic tori contained in Aut∗k k , and that every algebraic t...

Reconstruction results give conditions under which the abstract group structure of the automorphism group Aut(M) of an ω-categorical structure M determines the topology on Aut(M), and hence determines M up to biinterpretability, by [1]; they can also give conditions under which the abstract group Aut(M) determines the permutation group 〈Aut(M),M〉, so determines M up to bi-definability. One such...