Representation of Group Elements as Short Products

László Babai, P. Erdős

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We prove that every group G of order n has t≤logn/log2 + 0(log log n) elements x1,...,x1 such that every group element is a product of the form xt1 1...xt1 1, e{open} {0.1}. The result is true more generally for quasigroups. As a corollary we obtain that for n even, every one-factorization of the complete graph on n vertices contains at most t one-factors whose union is connected.

Original languageEnglish
Pages (from-to)27-30
Number of pages4
JournalNorth-Holland Mathematics Studies
Volume60
Issue numberC
DOIs
Publication statusPublished - 1982

ASJC Scopus subject areas

  • Mathematics(all)

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