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### Intersection of Normal Subgroups

```
Date: 03/18/99 at 12:58:12
From: David Bemis
Subject: Sub-groups

Show that the intersection of two normal subgroups of G is a normal
subgroup of G. I really do not know where to begin!

Thanks.
```

```
Date: 03/18/99 at 15:17:38
From: Doctor Rob
Subject: Re: Sub-groups

Start with the definition of a normal subgroup N of a group G. N is
normal if and only if for every n in N and every g in G, g^(-1)*n*g
is in N.

Next, let H and K be two normal subgroups of G, and let M be the
intersection of H and K. You want to show that M is normal. Take any
element n in N. Then n is in H and also n is in K. Use the fact that
H and K are normal to say things about g^(-1)*n*g, and conclude that
this element is in N, no matter what g in G is chosen.

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Modern Algebra

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