True or False? 1. Let G be a group and H a nonempty subset of G. If ab-1 is in H whenever a and b are in H, then H is a subgroup of G. 6Z < 3Z under addition. 2. 3. Let G be a group and let a be one fixed element of G. Then the set {x € G| ax = xa} is a subgroup of G.
True or False? 1. Let G be a group and H a nonempty subset of G. If ab-1 is in H whenever a and b are in H, then H is a subgroup of G. 6Z < 3Z under addition. 2. 3. Let G be a group and let a be one fixed element of G. Then the set {x € G| ax = xa} is a subgroup of G.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 10TFE
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