Let G = {(1) (2) (3) (4), (12) (3) (4) , (1) (2) (34), (12) (34)} with operation multiplication. a. Construct a multiplication table for G. b. Find an automorphism f: G→ G satisfying f[(12) (3) (4)] = ( 1) (2) (34) and f[( 1 ) ( 2 ) ( 34 )] = ( 1 2 ) ( 3 ) ( 4 ).
Let G = {(1) (2) (3) (4), (12) (3) (4) , (1) (2) (34), (12) (34)} with operation multiplication. a. Construct a multiplication table for G. b. Find an automorphism f: G→ G satisfying f[(12) (3) (4)] = ( 1) (2) (34) and f[( 1 ) ( 2 ) ( 34 )] = ( 1 2 ) ( 3 ) ( 4 ).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let G = {(1) (2) (3) (4), (12) (3) (4)
, (1) (2) (34), (12) (34)} with
operation multiplication.
a. Construct a multiplication table for G.
b. Find an automorphism f: G→ G
satisfying
f[(12) (3) (4)] = (1) (2) (34) and
f[( 1 ) ( 2 ) ( 34 )] = ( 1 2 ) ( 3 ) ( 4 ).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a5ac2db-d584-49da-a0ed-efa785bd6c28%2Fbb7ce6c5-e957-419d-a7d3-3cdb66687dfa%2F2h7pltc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let G = {(1) (2) (3) (4), (12) (3) (4)
, (1) (2) (34), (12) (34)} with
operation multiplication.
a. Construct a multiplication table for G.
b. Find an automorphism f: G→ G
satisfying
f[(12) (3) (4)] = (1) (2) (34) and
f[( 1 ) ( 2 ) ( 34 )] = ( 1 2 ) ( 3 ) ( 4 ).
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