One of the main problem in group theory is to classify groups upto isomorphisms. In this talk, we will classify all groups (up to isomorphisim) of order n under some conditions on n. More precisely, The cyclic group order of order n is the only group of order n (up to isomorphism) if and only if (n, φ(n)) = 1, where φ denotes the Euler-phi function and (n, φ(n)) denotes the gcd of n and φ(n). The proof which we shall see in this talk uses simple techniques, like semi-direct product and Sylow’s theorems etc.
This talk intended for masters-level students. It is fairly understandable by anyone who has background in group theory. So, all are welcome. Please use this opportunity.