Eseerise 5 (a) Prove that au is om isomoyihism y preserves ele ment's order, that is. 1ylasl= lal (6) Fix an element a in a p(x)=aza pis an isomorphism G>G. (c) Prove that I81=laba1 Va,BEG CG is a G. and define group xE G. Prove that group).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Modern Algebra:

 

Eseerise 5 (a) Prove that au
preserves element's order that is
(8) Fix au element a in a
isomoyihisme y
. Ip(a)l- lal.
G. and define
p(x)%3Daxa" p is an
isomorphism G
ograup
OXEG. Prove that
-2G
1-
acd
(c) Prave that 181=labal V a, be G
Prove
CGisa group).
Transcribed Image Text:Eseerise 5 (a) Prove that au preserves element's order that is (8) Fix au element a in a isomoyihisme y . Ip(a)l- lal. G. and define p(x)%3Daxa" p is an isomorphism G ograup OXEG. Prove that -2G 1- acd (c) Prave that 181=labal V a, be G Prove CGisa group).
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