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Dec. 2007 Sultan Almuhammadi ICS 555 LNGT IICCSS 555555 DDAATTAA SSEECCUURRIITTYY AANNDD CCRRYYPPTTOOGGRRAAPPHHYY
 

Summary: Dec. 2007 Sultan Almuhammadi ICS 555 LNGT
1
IICCSS 555555 DDAATTAA SSEECCUURRIITTYY AANNDD CCRRYYPPTTOOGGRRAAPPHHYY
Lecture Notes on Group Theory
1. Introduction to Groups
[1] Definition. A group (G, ) is a nonempty set G together with a binary operation on
G such that the following conditions hold:
(i) Closure: For all a,b G the element a b is a uniquely defined element of G
(ii) Associativity: For all a,b,c G, we have
a (b c) = (a b) c
(iii) Identity: There exists an identity element e G such that for all a G
e a = a and a e = a
(iv) Inverses: For each a G there exists an inverse element a-1
G such that
a a-1
= e and a-1
a = e
[2] Notations.
1. Juxtaposition: we usually write "ab" for the product (a b)
2. Power (Superscript): an

  

Source: Almuhammadi, Sultan - Department of Information and Computer Science, King Fahd University of Petroleum and Minerals

 

Collections: Computer Technologies and Information Sciences