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Subgroup of direct product

  • Thread starter POtment
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  • #1
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1. Homework Statement
Let G1, G2 be groups with subgroups H1,H2. Show that

[{x1,x2) | x1 element of H1, x2 element of H2} is a subgroup of the direct product of G1 X G2

3. The Attempt at a Solution
I'm not sure how to begin solving this problem.
 

Answers and Replies

  • #2
Dick
Science Advisor
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Show it the usual way you show a set is a subgroup. Show H1xH2 is closed under the group operation, that it has an identity, that it has inverses, etc.
 

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