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# homework2 - Math 113 Section 5 Fall 2010 Homework#2 Due...

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Math 113 Section 5 Homework #2 Fall 2010 Due: Monday, September 13 1. Determine which of the following sets with 2 -to- 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 > 0 , 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 2. Let ( G, · ) be a group.

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homework2 - Math 113 Section 5 Fall 2010 Homework#2 Due...

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