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a)Let G be a group of order pq, where p and q are primes. Prove that either G is abelian or Z(G) = {e}.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

a)Let G be a group of order pq, where p and q are primes. Prove that either G is abelian or Z(G) = {e}.

b)Let G be a group of order 12n, where n is a positive integer, n ≡ 1 mod 3. If H and K are subgroups of G of order 3, prove or disprove:

-If G is abelian, then H = K.

-If G is nonabelian, then H = K.

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