Chapter 1 Introduction

interest group, continue to maintain relatively good relations under the umbrella of critical race theory, meeting together at periodic conferences and gatherings, each has developed its own body of literature and set of priorities. For example, Latino and Asian scholars study immigration theory and policy, as well as

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A FRIENDLY INTRODUCTION TO GROUP THEORY 3 A good way to check your understanding of the above de nitions is to make sure you understand why the following equation is correct: jhgij= o(g): (1) De nition 5: A group Gis called abelian (or commutative) if gh = hg for all g;h2G. A group is called cyclic if it is generated by a single element, that is,

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example, in the group of all roots of unity in C each element has nite order. Theorem3.2gives a nice combinatorial interpretation of the order of g, when it is nite: the order of gis the size of the group hgi. In fact, this even works when ghas in nite order (then hgiis an in nite group), so the order of gis always the size of hgi.

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linear group of 2 by 2 matrices over the reals R. 3.The set of matrices G= ˆ e= 1 0 0 1 ;a= 1 0 0 1 ;b= 1 0 0 1 ;c= 1 0 0 1 ˙ under matrix multiplication. The multiplication table for this group is: e a b c e e a b c a a e c b b b c e a c c b a e 4.The non-zero complex numbers C …

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