series_homework - subgroups of G 2 Assume G is a Fnite...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework on Derived Series, and Upper and Lower Central Series April 12, 2010 1. We say that a subgroup H of a group G is characteristic if every auto- morphism σ : G G maps H H . Note that if G has only a single subgroup H of some order n , then H is characteristic. Show that the elements of the upper central series are all characteristic
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: subgroups of G . 2. Assume G is a Fnite group. Using the characterization of nipotent from class, prove that G is nilpotent if and only if G has a subgroup of each order dividing | G | . 3. ±ind the upper and lower central series for A 4 and S 4 . 1...
View Full Document

This note was uploaded on 10/23/2011 for the course MATH 4108 taught by Professor Staff during the Spring '10 term at Georgia Tech.

Ask a homework question - tutors are online