Intersection of Normal SubgroupsDate: 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/ |
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