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7. Let A:= {(1), (1, 2) (3, 4), (1, 3) (2, 4), (1,4) (2,3)}, b:= (1,2,3,4) and G:= Sym(4). (a) Show that A is a normal subgroup of G. (b) Compute the order of bA as an element of the group G/A.

7. Let A:= {(1), (1, 2) (3, 4), (1, 3) (2, 4), (1,4) (2,3)}, b:= (1,2,3,4) and G:= Sym(4). (a) Show that A is a normal subgroup of G. (b) Compute the order of bA as an element of the group G/A.

Elements Of Modern Algebra
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 22E
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7. Let A := {(1), (1, 2) (3, 4), (1, 3) (2, 4), (1, 4) (2,3)}, b:= (1, 2, 3, 4) and G:= Sym(4). (a) Show that A is a normal subgroup of G. (b) Compute the order of bA as an element of the group G/A.
Transcribed Image Text:7. Let A := {(1), (1, 2) (3, 4), (1, 3) (2, 4), (1, 4) (2,3)}, b:= (1, 2, 3, 4) and G:= Sym(4). (a) Show that A is a normal subgroup of G. (b) Compute the order of bA as an element of the group G/A.
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