THE GATEBOOK

Normalization Lectures

Let G be non-abelian group. is ---?

When n=1 the group is a trivial one. Now every group of prime order is cyclic and hence abelian. Hence groups of n=2,3 and 5 are abelian. Since every group of order p^2 (where p is prime) is abelian. Group of order 4= 2^2 is abelian. Hence every group of order less than or equal to 5 is abelian.

Therefore smallest is 6