The Groups and Nilpotent Lie Rings of Order p8 with Maximal Class (original) (raw)
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2020
Recall that a p-group of order p^ n >p^ 3 is of maximal class, if its nilpotency class is n-1. In this paper, we recall some preliminaries of nilpotent groups and give some basic material about p-groups of maximal class. Furthermore, we introduce the fundamental subgroup of a p-group of maximal class by specifying its importance in the general theory of p-groups of maximal class.
3 ADJOINT GROUPS OF p-NIL RINGS AND p-GROUP AUTOMORPHISMS
2016
We introduce a class of rings, namely the class of left or right p-nil rings, for which the adjoint groups behave regularly. Every p-ring is close to being left or right p-nil in the sense that it contains a large ideal belonging to this class. Also their adjoint groups occur naturally as groups of automorphisms of p-groups. These facts and some of their applications are investigated in this paper.
Some Applications of Two-Generator p-Groups of Nilpotency Class Two
2001
Klasifikasi bagi semua kumpulan dengan dua penjana yang mempunyai kelas nilpoten dua telah diperolehi oleh Nor Haniza Sarmin dalam tahun 2000. Kajian yang terdahulu bagi kumpulan terhingga telah dilakukan oleh Kappe et. al dalam tahun 1999 dan Bacon dan Kappe dalam tahun 1993. Kemudian, dalam tahun 2000, James Beuerle dan Kappe telah menumpukan klasifikasi mereka kepada kumpulan metakitaran tak terhingga dan beberapa aplikasinya. Penyelidikan ini ditumpukan kepada beberapa aplikasi bagi kumpulan-p dengan dua penjana termasuk kuasa dua tensor yang tak abelan dan kuasa dua peluaran. Kajian ini juga akan menentukan kumpulan berupaya dari kumpulan tersebut. Katakunci: Kuasa dua tensor yang tak abelan; kumpulan-dua; dua penjana; kelas nilpoten dua. The classification of all two-generator groups of nilpotency class two have been done by Nor Haniza Sarmin in 2000. Earlier research on the finite case was introduced by Kappe et. al in 1999 and Bacon and Kappe in 1993. Later, in 2000, James B...
On Classification of 9-Dimensional Nilpotent 3-ary Algebras of Class Two
Bulletin of the Iranian Mathematical Society, 2020
The nilpotent Filippov algebra of class two plays an essential role in some geometric problems, and the classification of nilpotent Lie algebras of class two is one of the most important issues in Lie algebras. In this paper, we classify 9-dimensional nilpotent 3ary algebras of class two over an arbitrary field.
On a Class of Generalized Nilpotent Groups
Journal of Algebra, 2002
We explore the class of generalized nilpotent groups in the universe c of all radical locally finite groups satisfying min-p for every prime p. We obtain that this class is the natural generalization of the class of finite nilpotent groups from the finite universe to the universe c. Moreover, the structure of-groups is determined explicitly. It is also shown that is a subgroup-closed c-formation and that in every c-group the Fitting subgroup is the unique maximal normal-subgroup.