Theorem 2. Let G, and G, be two groups. Let G = G,x G2 H = {(a,e,)\a e G} = G, x{e,} %3D and H, = {(e,.b)b eG,} = {e,)xG, then G is an internal direct product of H, and H,.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Theorem 2. Let G; and G, be two groups. Let G = G,x G2
H = {(a,e,)|a e G} = G x{e;}
%3D
H, = {(e.b)beG} = {e}xG,
and
then G is an internal direct product of H and H,.
Transcribed Image Text:Theorem 2. Let G; and G, be two groups. Let G = G,x G2 H = {(a,e,)|a e G} = G x{e;} %3D H, = {(e.b)beG} = {e}xG, and then G is an internal direct product of H and H,.
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