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# Chapter 02: Groups

Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN.

### Contents and summary

- Definition (axioms of group)
- Definition ( commutative group )
- Definition (idempotent)
- Properties of Group
- Theorem (The Cancellation Law)
- Theorem (Solution of Linear Equations )
- Subgroups
- Definition ( subgroup )
- Cyclic Groups
- Definition ( cyclic group )
- Cosets-Lagrange’s Theorem
- Permutations
- Cycles
- Transpositions
- Order of a Permutation
- Rings and Fields
- Properties of Rings

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