Thread: Non-abelian groups of order p^2 q

If |G| = p^2 q for two distinct primes p, q, then is G necessarily abelian? Are there any non-abelian groups of order p^2 q?

Originally Posted by prettyboy

If |G| = p^2 q for two distinct primes p, q, then is G necessarily abelian? Are there any non-abelian groups of order p^2 q?

of course! for example is non-abelian and its order is another example is the dihedral group of order 12. however, if G has order and then is abelian.

Refer the book ion abstract algebra by Dummit and Foote. a large behaviour of these groups are well explained