4. Consider the following groups G and H, K

Solve correctly ASAP Do both parts4. Consider the following groups G and H, K < G. If G is isomorphic to<br>H × K, give an isomorphism y : G → H × K. If not, say why G and<br>H × K cannot be isomorphic.<br>(a) G = R*, H = {1, –1}, K = R+<br>(b) G = D4, H = {1,r, r², r³}, K = {1, s}<br>%3D<br>

Extracted 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}="">

Jun 04, 2022
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