6. For a positive integer n 2 4 and a prime number psn, let U, denote the union of p,n all p-Sylow subgroups of the alternating group A, on n letters. Also let K, P, n denote the subgroup of A, generated by U. and let p, n Kpn denote the order of Kn. Then P, n . (a) K2,4| = 12 (b) |K2 4| = 4 (c) K2.5 = 60 (d) K3.5 = 30 \K3,5
6. For a positive integer n 2 4 and a prime number psn, let U, denote the union of p,n all p-Sylow subgroups of the alternating group A, on n letters. Also let K, P, n denote the subgroup of A, generated by U. and let p, n Kpn denote the order of Kn. Then P, n . (a) K2,4| = 12 (b) |K2 4| = 4 (c) K2.5 = 60 (d) K3.5 = 30 \K3,5
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 1E: 1. Consider , the groups of units in under multiplication. For each of the following subgroups in ,...
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