Frobenius-like groups as groups of automorphisms

Gülin ERCAN; İsmail Şuayip GÜLOĞLU; Evgeny KHUKHRO

Makale detayları

Frobenius-like groups as groups of automorphisms

Yazarlar:

Gülin ERCAN | İsmail Şuayip GÜLOĞLU | Evgeny KHUKHRO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 6, pp.965-976

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747242

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

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  FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G  admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting a Frobenius-like group of  automorphisms with fixed-point-free almost extraspecial kernel.

 

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  FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G  admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting a Frobenius-like group of  automorphisms with fixed-point-free almost extraspecial kernel.

Makale detayları

Frobenius-like groups as groups of automorphisms

Yazarlar:

Gülin ERCAN | İsmail Şuayip GÜLOĞLU | Evgeny KHUKHRO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 6, pp.965-976

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747242

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Frobenius group

Frobenius-like group

fixed points

Fitting height

nilpotency class

derived length

rank

order

Sayı

Makale detayları

Yazarlar: Gülin ERCAN | İsmail Şuayip GÜLOĞLU | Evgeny KHUKHRO

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2014 Vol.38 Issue 6, pp.965-976

Belge Tipi: Makale

Yayın Tarihi: 5/2014

Belge Dili: Türkçe

Document ID (Org No.): 2000747242

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Gülin ERCAN | İsmail Şuayip GÜLOĞLU | Evgeny KHUKHRO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 6, pp.965-976

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747242

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098