Euler Characteristic of Groups – C.T.C. Wall’s Approach

ABSTRACT: This work concentrates on the Euler characteristic of groups and points out that, this number can also be a rational one. We give some background material on the Euler theorem and the relevant topics. We also review the Fundamental Group and the Covering Space theories. We give C.T.C. Wall’s definition for the Euler characteristic of a group. We fill in the gaps in the proofs of certain formula given under the notions of L-class and M-class. Finally, we describe the exact structure of subgroups of free products of groups via some examples. Keywords: Euler characteristic, Euler theorem, Fundamental Group Theory, Covering Space Theory, C.T.C. Wall’s definition, L-class, M-class, free products of groups. ……………………………………………………………………………………………………………………………………………………………………………………………………………………