Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a = e a^4 = e a^3 = e O a^2 = e Let (G1, •) and (G2, *) be two groups and p: G1→ G2 be an isomorphism. Then * G2 is abelian if and only if G1 is cyclic. G2 might be abelian even if G1 is abelian : O G2 is cyclic if G1. lic.

Suppose that f: G → G such that f(x) = axa. Then fis a group homomorphism if and only if a = e a^4 = e a^3 = e O a^2 = e Let (G1, •) and (G2, ) be two groups and p: G1→ G2 be an isomorphism. Then G2 is abelian if and only if G1 is cyclic. G2 might be abelian even if G1 is abelian : O G2 is cyclic if G1. lic.

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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Question

36
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Suppose that f:G → G such that f(x) = axa. Then fis a group homomorphism if
and only if
a = e
a^4 = e
a^3 = e
O a^2 = e
Let (G1, •) and (G2 , *) be two groups and
p: G1→ G2 be an isomorphism. Then *
G2 is abelian if and only if G1 is cyclic.
G2 might be abelian even if G1 is abelian
G2 is cyclic if G1 ,
lic.

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