Given a subgroup , consider the set . Prove that is normal if and only if .
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Originally Posted by JJMC89 Given a subgroup , consider the set . Prove that is normal if and only if . This is by definition isn't it......namely is the largest subgroup (and yes, it is always a subgroup) such that
Originally Posted by Drexel28 This is by definition isn't it......namely is the largest subgroup (and yes, it is always a subgroup) such that The only definition I have for the normalizer is that it is the set .
Originally Posted by JJMC89 The only definition I have for the normalizer is that it is the set . I mean for normality. One has that if and only if for all which is precisely saying that .
Originally Posted by Drexel28 I mean for normality. One has that if and only if for all which is precisely saying that . Oh right. I've got it now.
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