NORMAL CAYLEY GRAPHS OF CERTAIN GROUPSWHICH ARE LOCALLY PRIMITIVE

In this paper we consider a certain group of order 8n and prove thatit is never an X-locally primitive normal connected Cayley graph of valency atleast 3

Finite edge-transitive dihedrant graphs

AbstractIn this paper, we first prove that each biquasiprimitive permutation group containing a regular dihedral subgroup is biprimitive, and then give a classification of such groups. The classification is then used to classify vertex-quasiprimitive and vertex-biquasiprimitive edge-transitive dihedrants. Moreover, a characterization of valencies of normal edge-transitive dihedrants is obtained, and some classes of examples with certain valences are constructed

Product of Locally Primitive Graphs

Many large graphs can be constructed from existing smaller graphs by using graph operations, such as the product of two graphs. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this paper we consider the product of two locally primitive graphs and prove that only tensor product of them will also be locally primitive

On the Finiteness of the Classifying Space for Virtually Cyclic Subgroups

This thesis mainly deals with finiteness properties of the classifying space for the family of virtually cyclic subgroups. We establish a link between the finiteness of the classifying space and the conjugacy growth invariant of the given group and use this connection to show that the classifying space for virtually cyclic subgroups is not of finite type except in trivial cases if the group is linear or a CAT(0) cube group. We also investigate the class of residually finite groups in this context and along the way come close to a classification of the finite groups which have only two conjugacy classes of maximal cyclic subgroups

Computational Group Theory (hybrid meeting)

This was the eighth Oberwolfach Workshop on Computational Group Theory. It demonstrated how an increasing number and variety of deep theoretical results are being used to devise powerful and practical algorithms in Computational Group Theory. The talks also presented connections with and applications to Number Theory, Combinatorics, Geometry, and Geometric Group Theory