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(a) Prove that if K is a subgroup of G and L is a subgroup of H, then K x L is a subgroup of G x H.

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

Let G and H be groups. Consider the Cartesian product G x H.
(a) Prove that if K is a subgroup of G and L is a subgroup of H, then K x L is a subgroup
of G x H.
(b) Prove that G x H is a commutative group if and only if both G and H are commutative
groups.

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