(a) Let H G, K G. Show that H V K is normal in G....

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(a) Let H ◁ G, K ◁ G. Show that H V K is normal in G.
(b) Prove that the set of all normal subgroups of G forms a complete lattice under inclusion (Introduction, Exercise 7.2).

Exercise 7.2

Let G be a finite group and-Ha subgroup of G of order n. If His the only subgroup of G of order n, then His normal in G.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 13, 2023 03:07 AM

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(a) Let H G, K G. Show that H V K is normal in G....

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a To show that H V K is normal in G we need to show that for any g in G gH V Kg1 is a subset of H V ...View the full answer

Algebra Graduate Texts In Mathematics 73

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