Quick question about subgroups and external direct products

Thread starter wakko101
Start date Mar 8, 2010

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If A and B are groups, then the external direct product A x B is indeed a group. For subgroups A' of A and B' of B, the product A' x B' is a subgroup of A x B if it contains the identity element, is closed under multiplication componentwise, and includes inverses. The discussion emphasizes the importance of these properties to confirm that A' x B' is a subgroup. Therefore, the conditions for subgroup formation in the context of direct products are crucial for validating subgroup status. Understanding these criteria is essential for group theory applications.

Mar 8, 2010

wakko101

If A and B are groups, then A x B is a group...does the same hold for subgroups? i.e. if A' is a subgroup of A and B' for B, then is A' x B' a subgroup of A x B?

Cheers,
W. =)

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Mar 8, 2010

Tinyboss

Well, does it contain the identity? Is it closed under multiplication (componentwise)? Inverses?

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