Group automorphism, Mathematics

(a) Find an example of groups G, H, K with K 2325_Group automorphism.png H and H 2325_Group automorphism.png G but K 1662_Group automorphism1.png G.

(b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that every characteristic subgroup is normal.

(c) Show that if K ⊆ H ⊆ G, K is characteristic in H and H is characteristic in G then K is characteristic in G.

(d) Show that Dn(G) is normal in all of G not just in Dn-1(G).

(e) Conclude that G is solvable i it has a subnormal series in which each quotient is abelian and each group in the series is normal in all of G.

If G is a group, an automorphism of the form 1184_Group automorphism2.png is called an inner automorphism. An automorphism not of this form is called outer.

The aim of the following questions is to show that all the automorphisms of Sn are inner, except for S6 which does have an outer automorphism.

Posted Date: 2/26/2013 3:03:17 AM | Location : United States







Related Discussions:- Group automorphism, Assignment Help, Ask Question on Group automorphism, Get Answer, Expert's Help, Group automorphism Discussions

Write discussion on Group automorphism
Your posts are moderated
Related Questions



if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3


what is division

Algebraic Word Problems: Equations: 1. The total electrical output of one nuclear facility is 200 megawatts more than that of another nuclear facility. Let L be the

Marginal cost & cost function  The cost to produce an additional item is called the marginal cost and as we've illustrated in the above example the marginal cost is approxima

write the zeros of underroot3power2 -8x+4underroot 3