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Unformatted text preview: Math 113 Section 5 Homework #2 Fall 2010 Due: Monday, September 13 1. Determine which of the following sets with 2to 1 operations form groups. For those that are groups, prove that they are groups. For those that are not groups, describe why they are not groups. (a) Z with usual addition + (b) Z with usual multipication (c) Z /n Z where n is any positive integer, with multiplication (d) ( Z /n Z ) , the set of invertible elements of Z /n Z , with multiplication (e) M n m , the set of n m matrices with entries in R , with matrix addition (f) M n m , the set of n m matrices with entries in R , with matrix multiplication (g) M n , the set of (square) n n matrices with entries in R , with matrix multiplication (h) G = { a + b 2  a,b Q } R with multiplication (i) G = { z C  z n = 1 } , where n Z > , with multiplication of complex numbers (j) Q where a b is given in lowest terms and is defined by a b c d = a + c b + d , reduced to lowest terms...
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This note was uploaded on 01/21/2012 for the course MATH 113 taught by Professor Ogus during the Fall '08 term at University of California, Berkeley.
 Fall '08
 OGUS
 Algebra, Sets

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