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1. Consider the following groups G and H, K < G. If G is isomorphic to H × K, give an isomorphism v : G → H × K. If not, say why G and H × K cannot be isomorphic. (a) G = R*, H = {1,–1}, K = R+ (b) G = D4, H = {1,r, r² , r³}, K = {1, s}

1. Consider the following groups G and H, K < G. If G is isomorphic to H × K, give an isomorphism v : G → H × K. If not, say why G and H × K cannot be isomorphic. (a) G = R*, H = {1,–1}, K = R+ (b) G = D4, H = {1,r, r² , r³}, K = {1, s}

Advanced Engineering Mathematics
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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4. Consider the following groups G and H, K < G. If G is isomorphic to H × K, give an isomorphism y : G → H × K. If not, say why G and H × K cannot be isomorphic. (a) G = R*, H = {1, –1}, K = R+ (b) G = D4, H = {1,r, r², r³}, K = {1, s} %3D
Transcribed Image Text:4. Consider the following groups G and H, K < G. If G is isomorphic to H × K, give an isomorphism y : G → H × K. If not, say why G and H × K cannot be isomorphic. (a) G = R*, H = {1, –1}, K = R+ (b) G = D4, H = {1,r, r², r³}, K = {1, s} %3D
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