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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