Department of Mathematics

Indian Institute Of Technology Madras , Chennai

Existence of a unique group of finite order

Speaker : Jayakumar, Research scholar, IMSc, Chennai


Abstract :

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.

Key Speaker Jayakumar, Research scholar, IMSc, Chennai
Place NAC 519
Start Time 3:00 PM
Finish Time 4:00 PM
External Link None