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Introduction to elementary group theory



Group theory is the study of algebraic structures called groups. This theory will rely heavily on set theory and modular arithmetic as well . It will require an understanding of mathematical induction, functions, bijections, and partitions. It may utilize matrices and complex numbers as well.
Set is one of the most important concept in modern mathematics. It alone conveys very limited information . It becomes more meaningful if we can relate or do something with or operate on its members or elements.

The simplest way is to relate or combine an element of a set with itself and get the same or a different element of the same set.

for instances,1 times 1 gives 1 ; whereas 1 added to 1 gives 2,a different number.

We can also relate or combine an element of a set with a different element of the set and arrive at one of the numbers or completely different number.

For example, 2 times 3 is 6 ;whereas 2 added to 3 is 5 ,which is completely different number.

Note: In all cases the resulting number belongs to the same original set or set under reference.

We have used multiplication and addition operation on the set of counting numbers.