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# Mathematical Method Notes: Chapter 02 – Groups

If your finding Mathematical Method notes for chapter 2 – Groups for help you prepare for exams? if am right, then your in the right place to examine and download the necessary mathematical methods notes. All these method notes of BSc/ADS, our teacher wrote these notes so that they can study them for the end-of-term exam. You can obtain the necessary material in PDF files on the online learning platform known as Study Medium. Additionally, please get in touch with us. Your remarks and total citations will be published.

A set and a binary operation come together to form a group. As an illustration, the collection of integers with an addition operation forms a group, as does the set of real numbers with a binary addition process.

## Course Contents

• Definition (axioms of the 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

## Mathematical Method Notes By Prof Naeem-Ul-Haq

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