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How Abelian is a Finite Group?

  • Lásló Pyber
Chapter

Summary.

The first paper with the above title was written by Erdős and Straus. Here we solve one of the problems considered there by proving that every group of order n contains an abelian subgroup of order at least \({2}^{\varepsilon \sqrt{\log n}}\) for some \(\varepsilon > 0\). This result is essentially best possible.We also give a quick survey of recent developments in related areas of group theory which were greatly stimulated by questions of Erdős.

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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