College Algebra Exam Review 141

College Algebra Exam Review 141 - 3.1. DIRECT PRODUCTS 151...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3.1. DIRECT PRODUCTS 151 Since the Q A i are mutually commuting subgroups, the subgroup gener- ated by any collection of them is their product: h Q A i 1 ; Q A i 2 ::::; Q A i s i D Q A i 1 Q A i 2 Q A i s : In fact, the product is f .x 1 ;x 2 ;:::;x n / 2 P W x j D e if j 62 f i 1 ;:::;i s gg : In particular, Q A 1 Q A 2 Q A n D P . Example 3.1.11. Suppose the local animal shelter houses several collec- tions of animals of different types: four African aardvarks, five Brazilian bears, seven Canadian canaries, three Dalmatian dogs, and two Ethiopian elephants, each collection in a different room of the shelter. Let A denote the group of permutations of the aardvarks, A S 4 . 1 Likewise, let B denote the group of permutations of the bears, B S 5 ; let C denote the group of permutations of the canaries, C S 7 ; let D denote the group of permutations of the dogs, D S 4 ; and finally, let E denote the group of permutations of the elephants, E S 2 Z 2 . The symmetry group of the entire zoo is...
View Full Document

This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.

Ask a homework question - tutors are online