3) a) Explain how many distinct necklaces of 11 red and green beads are possible? b) Prove that a group G of order 24 must have a normal subgroup of order 4 or 8. -7- [Hint: Consider a Sylow 2-subgroup P of G, and the action of G on the cosets G/P.]
3) a) Explain how many distinct necklaces of 11 red and green beads are possible? b) Prove that a group G of order 24 must have a normal subgroup of order 4 or 8. -7- [Hint: Consider a Sylow 2-subgroup P of G, and the action of G on the cosets G/P.]
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 21E
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