Action of a Frobenius-like group with kernel having central derived subgroup


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Ercan G. , Güloğlu İ. Ş.

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, cilt.26, ss.1257-1265, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 26
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0218196716500533
  • Dergi Adı: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
  • Sayfa Sayıları: ss.1257-1265

Özet

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.