The Generalization of the Exterior Square of a Bieberbach Group with Symmetric Point Group

Nor'ashiqin Mohd. Idrus, Tan Yee Ting, Rohaidah Masri, Nor Haniza Sarmin, Hazzirah Izzati Mat Hassim

Abstract


The exterior square is a homological functor originated in the homotopy theory, while Bieberbach groups with symmetric point group are torsion free crystallographic groups. In this paper, the generalization of the exterior square of a Bieberbach group with symmetric point group is constructed up to finite dimension.


Keywords


Exterior square; Bieberbach group; symmetric point goup

Full Text:

PDF

References


G. Ellis, On the computation of certain homotopical functors, LMS Journal of Computation and Mathematics 1 (1998), 25-41.

R. Brown and J. L. Loday, Van kampen theorems for diagrams of spaces, Topology 26 (1987), 311-335.

Y. T. Tan, N. Mohd. Idrus, R. Masri, W. N. F. Wan Mohd Fauzi, N. H. Sarmin and H. I. Mat Hassim, The nonabelian exterior square of a Bieberbach group with symmetric point group of order six. (Accepted by Journal of Science and Mathematics)

N. R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. (N. S.) 22 (1991), 63-79.

G. Ellis and F. Leonard, Computing Schur multipliers and tensor products of finite groups, Proc. Roy. Irish Acad. 95A(2) (1995), 137-147.

Y. T. Tan, N. Mohd. Idrus, R. Masri, N. H. Sarmin and H. I. Mat Hassim, On the generalization of some homological functors of a Bieberbach group with symmetric point group. (Submitted to Bulletin of the Malaysian Mathematical Sciences Society)




DOI: http://dx.doi.org/10.26713%2Fjims.v8i4.559

eISSN 0975-5748; pISSN 0974-875X