a) A 4 is not the direct product of its Sylow subgroups, but A 4 does have the property mn 12 and (m,n) 1 imply there is a subgroup of order m (b) S 3 has subgroups of orders 1, 2, 3, and 6 but is not the direct product of its Sylow subgroups ...

a To show that A4 is not the direct product of its Sylow subgroups note that A4 has two Sylow 3subgr ...

{a) A 4 is not the direct product of its Sylow subgroups, but A 4 does have

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{a) A₄ is not the direct product of its Sylow subgroups, but A₄ does have the property: mn = 12 and (m,n) = 1 imply there is a subgroup of order m.

(b) S₃ has subgroups of orders 1, 2, 3, and 6 but is not the direct product of its Sylow subgroups.

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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 14, 2023 12:06 PM

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{a) A 4 is not the direct product of its Sylow subgroups, but A 4 does have

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Algebra Graduate Texts In Mathematics 73

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