Idempotent transformations of finite groups

M. Blomgren, W. Chachólski, E. D. Farjoun, Y. Segev

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We describe the action of idempotent transformations on finite groups. We show that finiteness is preserved by such transformations and enumerate all possible values such transformations can assign to a fixed finite simple group. This is done in terms of the first two homology groups. We prove for example that except special linear groups, such an orbit can have at most 7 elements. We also study the action of monomials of idempotent transformations on finite groups and show for example that orbits of this action are always finite.

Original languageEnglish
Pages (from-to)56-86
Number of pages31
JournalAdvances in Mathematics
Volume233
Issue number1
DOIs
StatePublished - 1 Jan 2013

Keywords

  • Cellularization of groups
  • Simple groups

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