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# Tag Archives: group action

## Sylow’s Theorem, from the book

The most important theorems of elementary group theory are those of Lagrange and Sylow. I want to describe here what I consider the most beautiful proof of the first part of Sylow’s Theorem, actually based on Sylow’s original proof. But … Continue reading

## Notes on finite groups

As an escape from having too much to do, I have combined and lightly revised the notes from my MSc course on finite groups, and posted them here. I tried to steer a middle course between soluble groups and simple … Continue reading

Posted in exposition
Tagged composition series, extension theory, group action, Jordan-Holder Theorem, simple groups, Sylow's theorem
2 Comments

## The definition of a group

You might think that, by contrast to the case of a graph, the definition of a group would be quite clear-cut. Traditionally there are four axioms. A group is a set G with a binary operation • satisfying closure: for … Continue reading

Posted in exposition
Tagged Csaba Szabo, exchange property, group action, independence algebra, vector space
3 Comments