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Unformatted text preview: psubgroups of G . (h) If G and H are nite groups of the same order, then, for every prime p , their Sylow psubgroups have the same order. (i) There is a group of order 400 having exactly 8 Sylow 5subgroups. [9 pts] 2. Give an example of a nite group G having 3 Sylow psubgroups (for some prime p ) P , Q and R such that P Q = { e } and P R 6 = { e } . [3 pts] 3. Prove that there are no simple groups of order 300, 312, 616 or 1000. [3 pts]...
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This note was uploaded on 04/19/2011 for the course MATH 21373 taught by Professor Johnson during the Spring '11 term at Carnegie Mellon.
 Spring '11
 Johnson
 Algebra

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