your a) G = (Z12,O); H = {0,2,4, 6, 8, 10} %3D
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 11E: Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?
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Please use this theorem to solve the attached problem, thanks!
Theorem 5.1 Let H be a nonempty subset of a group G. Then H is a subgroup of G if and only if the following two conditions are satisfied:
i) for all a,b in H, ab is also in H, and
ii) for all a in H, a^-1 is also in H
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