and . Show that . Deduce that if , then

If , then if .

.

How can I get to the point where they are equal with this information?

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- Oct 8th 2011, 04:18 PMdwsmithNormalizer and Centralizer
and . Show that . Deduce that if , then

If , then if .

.

How can I get to the point where they are equal with this information? - Oct 8th 2011, 08:15 PMDevenoRe: Normalizer and Centralizer
well it's obvious that is a subgroup of . so what we need to show is that the normalizer is a subgroup of the centralizer if |H| = 2.

so let g be in . clearly , and we know that , where h is the non-identity element of H.

but if , then gh = g, and thus h = e, contradiction. hence , so - Oct 8th 2011, 08:15 PMdwsmithRe: Normalizer and Centralizer