{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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a To show that A4 is not the direct product of its Sylow subgroups note that A4 has two Sylow 3subgr...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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