Group Theory (ePub)

By many expert mathematicians, group theory is often
addressed as a central part of mathematics. It finds its origins
in geometry, since geometry describes groups in a detailed
manner. The theory of polynomial equations also describes the
procedure and principals of associating a finite group with any
polynomial equation. This association is done in such a way
that makes the group to encode information that can be used
to solve the equations. This equation theory was developed by
Galois. Finite group theory faced a number of changes in near
past times as a result of classification of finite simple groups.
The most important theorem when practicing group theory is
theorem by Jordan holder. This theorem shows how any finite
group is a combination of multiple finite simple groups.
Group theory is a term that is mainly used fields related to
mathematics such as algebraic calculations. In abstract algebra,
groups are referred as algebraic structures. Other terms of
algebraic theories, such as rings, fields and vector spaces are
also seen as group. Of course with some additional operations
and axioms, mathematicians accept them as a group. The
methods and procedures of group theory effect many parts
and concepts of mathematics as well as algebra on a large
scale. Linear algebraic groups and lie groups are two main
branches or say categories of group theory that have advanced
enough to be considered as a subject in their own
perspectives.
Not only mathematics, group theory also finds its roots in
various physical systems, especially in crystals and hydrogen
atom. They might be modeled by symmetry groups. Thus it
can be said that group theory possess close relations with
representation theory. Principals and ideas of group theory are
practically applied in the fields of physic, material science and
chemistry of course. Group theory is also considered as a
central key in the studies and practices of cryptography. In
2000s, more than 10000 pages were published in the time
span of 1960 to 1980. These publications were a collaborative
effort in order to culminating the result as a complete
classification of infinite simple groups. For the practitioners and
learners of mathematics or even physics the theory of groups
has a great importance. Not all aspects of this theory are used
in mathematics or physics. But there are some ideas and
principals that help a lot as you advance to higher level
mathematics, it is very same with the physics. Full application of
this wide theory is not possible on a single subject anyhow.
However it is partially applied in both cases, and still leaves a
great influence.