Abelian JSJ decomposition of graphs of free abelian groups

NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS

Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.  

NORMAL 6-VALENT CLAYEY GRAPHS OF ABELIAN GROUPS

We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aunt(Γ). in this paper, we give a classification of all non-normal Clayey graphs of finite abelian group with valency 6. 

JSJ-Decompositions of Coxeter Groups over Virtually Abelian Splittings

The idea of “JSJ-decompositions” for 3-manifolds began with work of Waldhausen and was developed later through work of Jaco, Shalen and Johansen. It was shown that there is a finite collection of 2-sided, incompressible tori that separate a closed irreducible 3-manifold into pieces with strong topological structure. Sela introduced the idea of JSJ-decompositions for groups, an idea that has flo...

Intuitionistic Free Abelian Groups

Decomposition of Elements in Abelian Groups*

In the present paper we determine necessary and sufficient conditions for an abelian group to have the property Pw . The author first proved the validity of these conditions for fields, but, as noted by T. Nakayama, the operation X does not occur, so that the theory may be stated for a system of elements with only one operation + defined for these elements. Groups with the property Pn have usef...