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Uses of Sylow Theory

Published online by Cambridge University Press:  03 November 2016

Joseph J. Malone Jr.
Joseph J. Malone Jr.*
Affiliation:
Dept. of Mathematics University of Houston, Houston 4Texas
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Extract

One approach to investigating the structure of a group is to examine the family of subgroups of the group. In particular, one often looks for normal subgroups and considers things such as direct products and composition series. However, fruitful investigation usually involves establishing that certain subgroups do, in fact, exist. Hence it is important to find conditions which will guarantee the existence of subgroups. This note indicates the usefulness of one such set of conditions—the Sylow theorems for finite groups.

Type
Research Article
Information
The Mathematical Gazette , Volume 51 , Issue 375 , February 1967 , pp. 11 - 14
Copyright
Copyright © Mathematical Association 1967

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References

1. Ledermann, Walter, Introduction to the Theory of Finite Groups, 3rd ed. revised,Oliver and Boyd, Edinburgh, 1957.Google Scholar
2. Malone, Joseph J. Jr., Sylow theory, Pi Mu Epsilon J., 3 (1963) 404–408.Google Scholar
3. Burnside, W., Theory of Groups of Finite Order, 2nd ed., University Press, Cambridge, 1911.Google Scholar