کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4584719 | 1630502 | 2014 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Derived length of a Frobenius-like kernel
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F called kernel which has a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a Frobenius-like group FH acts faithfully by linear transformations on a vector space V over a field of characteristic that does not divide |FH|. It is proved that the derived length of the kernel F is bounded solely in terms of the dimension m=dimCV(H) of the fixed-point subspace of H by g(m)=3+[log2(m+1)]. It follows that if a Frobenius-like group FH acts faithfully by coprime automorphisms on a finite group G, then the derived length of the kernel F is at most g(r), where r is the sectional rank of CG(H). As an application, for a finite solvable group G admitting an automorphism Ï of prime order coprime to |G|, a bound for the p-length of G is obtained in terms of the rank of a Hall pâ²-subgroup of CG(Ï). Earlier results of this kind were known only in the special case when the complement of the acting Frobenius-like group was assumed to have prime order and its fixed-point subspace (or subgroup) was assumed to be one-dimensional (or have all Sylow subgroups cyclic).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 412, 15 August 2014, Pages 179-188
Journal: Journal of Algebra - Volume 412, 15 August 2014, Pages 179-188
نویسندگان
Gülin Ercan, Ä°smail Å. GüloÄlu, Evgeny Khukhro,