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3.4. Let G, H be groups, and assume that G H x G. Can you conclude that H is trivial? (Hint: No. Can you construct a counterexample?)

3.4. Let G, H be groups, and assume that G H x G. Can you conclude that H is trivial? (Hint: No. Can you construct a counterexample?)

Advanced Engineering Mathematics
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: 3.3. Show that if G, H are abelian groups, then G x H satisfies the universal property for coproducts in Ab (cf. §I.5.5). [§3.5, 3.6, §III.6.1] 3.4. Let G, H be groups, and assume that G H x G. Can you conclude that H is trivial? (Hint: No. Can you construct a counterexample?)
Transcribed Image Text:Question: 3.3. Show that if G, H are abelian groups, then G x H satisfies the universal property for coproducts in Ab (cf. §I.5.5). [§3.5, 3.6, §III.6.1] 3.4. Let G, H be groups, and assume that G H x G. Can you conclude that H is trivial? (Hint: No. Can you construct a counterexample?)
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