How Abelian is a Finite Group?

Lásló Pyber ()
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Lásló Pyber: Mathematical Institute of the Hungarian Academy of Sciences

A chapter in The Mathematics of Paul Erdős I, 2013, pp 409-423 from Springer

Abstract: 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.

Keywords: Abelian Subgroup; Abelian Section; Shanskii; Soluble Groups; Wiegold (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_25

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DOI: 10.1007/978-1-4614-7258-2_25

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