(a) Show that if q: G G' is a homomorphism of groups, then H = ker(p)...

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(a) Show that if q: G→ G' is a homomorphism of groups, then H = ker(p) has the property that NG(H) = G. (b) Conclude that if G = D2n = (r, s Irn = s2 = 1, rs = sr-1) for n > 2, then there does not exist a group homomor- phism Q: D2n →G' to another group G' such that ker(p) = {1, s). (a) Show that if q: G→ G' is a homomorphism of groups, then H = ker(p) has the property that NG(H) = G. (b) Conclude that if G = D2n = (r, s Irn = s2 = 1, rs = sr-1) for n > 2, then there does not exist a group homomor- phism Q: D2n →G' to another group G' such that ker(p) = {1, s).

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a To show that NGH G we need to prove two inclusions NGH G If g NGH then gHg H This means that g is ... View the full answer