On the nature of finite groups

Details On the nature of finite groups On the nature of finite groups

2004-08-16

arxiv.org/abs/math/0408202v2

Mathematics

General Mathematics

4 pages, Latex2e

Scientific paper

The reality of the difficulties in investigation of finite groups are considered. It is shown that the consideration of symmetry properties of the $k$-orbits that are obtained with an action of a finite group $F=(V,\cdot)$ on Cartesian power $V^k$ gives a new view on the nature of groups and simplifies some difficult properties of groups. Using this representation it is obtained a simple proof of the W. Feit, J.G. Thompson theorem: Solvability of groups of odd order.

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