Divisibility in certain automorphism groups

Automorphism Groups of Certain Unstable Graphs

The automorphism groups of the canonical double covers of the unstable graphs in two infinite families are considered. These graphs are important from the point of view of algebraic map theory as they can be embedded into regular oriented maps.

The Automorphism Groups of a Certain Class

non-divisibility for abelian groups

Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting   all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...

Allan Adler Automorphism Groups of Certain Hypersurfaces Ii

In this article, we determine the automorphism groups of a family of cubic hypersurfaces generalizing those introduced in part I. Along the way, we determine all algebraic groups which contain PSL2(Fq) and which lie in PGLn(C), where q = 2n ± 1. This is accomplished using the classification of finite simple groups, information from the ATLAS of finite simple groups, the degrees of some complex ...

On divisibility in definable groups

Let M be an o–minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. In this note, we show that a definably compact definably connected group is divisible.