Nilpotent groups are round

Daniel Berend; Michael D. Boshernitzan

doi:10.1007/s11856-008-1040-z

Nilpotent groups are round

Daniel Berend
, Michael D. Boshernitzan

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of the group. Our main result is that this combinatorial property is equivalent to nilpotence.

Original language	English
Pages (from-to)	49-61
Number of pages	13
Journal	Israel Journal of Mathematics
Volume	167
Issue number	1
DOIs	https://doi.org/10.1007/s11856-008-1040-z
State	Published - 1 Oct 2008

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-008-1040-z

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AB - We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of the group. Our main result is that this combinatorial property is equivalent to nilpotence.

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Nilpotent groups are round

Abstract

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