Sept_Oct_2007_Summary

# Sept_Oct_2007_Summary - Summary of Some Research Findings...

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

Summary of Some Research Findings From Early Fall 2007 Nicholas Zoller Lehigh University Let G n,d be the n th group in the Magma/GAP database of transitive groups of degree d . Consider the minimal transitive group G 24 , 1489 found in the list in [2]. The center of G 24 , 1489 is trivial, so G 24 , 1489 cannot be the Galois group of a CM-ﬁeld. However, by looking at the minimal partitions of G 24 , 1489 , we can determine if it serves as a witness that another group of order 2 · | G 24 , 1489 | = 2 · 576 = 1152 is ρ -minimal. (See [1] for a deﬁnition and discussion of ρ -minimality). Magma veriﬁes that G 24 , 1489 has three minimal partitions, each consisting of 12 sets of imprimitivity of size 2. Call them P 1 , P 2 , and P 3 . Magma can ﬁnd the image and kernel of the action G 24 , 1489 on each of these block systems. Let K i and I i be the kernel and image, respectively of each of these actions, for i = 1 , 2 , 3 . Magma calculates that
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/29/2008 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University .

Ask a homework question - tutors are online