Unformatted text preview: subgroup of S n . (b) Prove that an inﬁnite simple group has no subgroups of ﬁnite index n > 1. 4. Leg G be a group with  G  = mp , where p is prime and 1 < m < p . Prove that G is not simple. 5. If n ≥ 3, prove that A n is the only subgroup of S n of order 1 2 n !. 6. Show that S 4 has a subgroup isomorphic to D 4 . 7. Prove that A 5 is a group of order 60 having no subgroup of order 30....
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 Spring '11
 Johnson
 Algebra, Normal subgroup, Subgroup, Cyclic group, Group isomorphism

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