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.

• 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