Abstract
In this paper, the most important liner groups are classified. Those that we often have the opportunity to meet when studying linear groups as well as their application in left groups. In addition to the introductory part, we have general linear groups, special linear groups, octagonal groups, symplicit groups, cyclic groups, dihedral groups: generators and relations. The paper is summarized with brief deficits, examples and evidence as well as several problems. When you ask why this paper, I will just say that it is one of the ways I contribute to the community and try to be a part of this little world of science.
Highlights
Algebra is the mathematical discipline that arose from the problem of solving equations [1]
If one starts with the integers Z, one knows that every equation a + x =b, where a and b are integers, has a unique solution
Let us enlarge Z to the rational numbers Q, consisting of all fraction’s c/d, where d ≠ 0. Both equations have a unique solution in Q, provided that a ≠ 0 for the equation ax = b
Summary
Algebra is the mathematical discipline that arose from the problem of solving equations [1]. Let us enlarge Z to the rational numbers Q, consisting of all fraction’s c/d, where d ≠ 0. Both equations have a unique solution in Q, provided that a ≠ 0 for the equation ax = b. For example, one takes the solutions of an equation such as x2 − 5 =0 and forms the set of all numbers of the form a + b 5 , where a and b are rational, we ( ) get a larger field, denoted by Q 5 , called an algebraic number field. Evariste Galois (1811-1832) coined the term group for these symmetries, and this group is called the Galois group of the field.
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