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Let A be a subgroup of G. (a) Prove that A's identity element is also G's identity element. (b) Show that for any a (as an element of A), a's inverse in A is the same as its inverse in G

Let A be a subgroup of G. (a) Prove that A's identity element is also G's identity element. (b) Show that for any a (as an element of A), a's inverse in A is the same as its inverse in G

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...
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Let A be a subgroup of G.
(a) Prove that A's identity element is also G's identity element.
(b) Show that for any a (as an element of A), a's inverse in A is the same as its inverse in G.

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