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Chapter 1 Group Fundamentals

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Book Id: WPLBN0000673785
Format Type: PDF eBook
File Size: 377.73 KB
Reproduction Date: 2005

Title: Chapter 1 Group Fundamentals  
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Chapter 1 Group Fundamentals. (n.d.). Chapter 1 Group Fundamentals. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: Groups and Subgroups. Definition A group is a nonempty set G on which there is defined a binary operation (a, b) - ab satisfying the following properties: Closure: If a and b belong to G, then ab is also in G; Associativity: a(bc) = (ab)c for all a, b, c E G; Identity: There is an element 1 in G such that a1 = 1a = a for all a in G; Inverse: If a is in G there is an element a?1 in G such that aa?1 = a?1a = 1. A group G is abelian if the binary operation is commutative, i.e., ab = ba for all a, b in G. In this case the binary operation is often written additively ((a, b) - a + b)), with the identity written as 0 rather than...


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