Action of a Frobenius-like group with fixed-point free kernel

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Ercan G., Güloğlu İ. Ş.

JOURNAL OF GROUP THEORY, cilt.17, ss.863-873, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1515/jgt-2014-0002
  • Dergi Adı: JOURNAL OF GROUP THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.863-873
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.