On Determinability of a Quotient Divisible Abelian Group of Rank 1 by Its Automorphism Group

THE AUTOMORPHISM GROUP OF NON-ABELIAN GROUP OF ORDER p^4

Let G be a finite non-abelian group of order p^4 . In this paper we give a structure theorem for the Sylow p-subgroup, Aut_p(G)  , of the automorphism group of G.

Fuzzy Subgroups of Rank Two Abelian p-Group

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

Splitting the Automorphism Group of an Abelian P-group

Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...

Characterization of C by its Automorphism Group

Let M be a connected complex manifold of dimension n and let Aut(M) denote the group of holomorphic automorphisms of M . The group Aut(M) is a topological group equipped with the natural compact-open topology. We are interested in the problem of characterizing M by Aut(M). This problem becomes particularly intriguing when Aut(M) is infinite-dimensional. Let, for example, M = C and suppose that ...

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group Or a Unitary Group