1) If (H, *) is a subgroups of (G, *)then (NG(H) , * ) is a subgroup of (G, *).

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1) If (H, *) is a subgroups of (G, *)then (NG(H) , * ) is a
subgroup of (G, *).
2) Let H={0,3 } , K={0,2,4}, such that (H,+6)& (K,+6)
are subgroups of (Z6 ,+6). Show that Z6 is an internal direct
product of H &K.
Transcribed Image Text:1) If (H, *) is a subgroups of (G, *)then (NG(H) , * ) is a subgroup of (G, *). 2) Let H={0,3 } , K={0,2,4}, such that (H,+6)& (K,+6) are subgroups of (Z6 ,+6). Show that Z6 is an internal direct product of H &K.
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