If (1) N G, then N = G; hence G is simple. [Use Exercise 18

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If (1) ≠ N ⊲ G, then N = G; hence G is simple. [Use Exercise 18 to show P < N; apply Exercise 19.]

Data from exercise 18

If (1) ≠ N ⊲ 1 G, then 7 divides |N|.

Data from exercise 19

The group G contains a subgroup P of order 7 such that the smallest normal subgroup of G containing P is G itself.

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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 16, 2023 03:56 AM

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If (1) N G, then N = G; hence G is simple. [Use Exercise 18

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Algebra Graduate Texts In Mathematics 73

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