nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2
نویسندگان
چکیده مقاله:
Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.
منابع مشابه
Bilinear cryptography using finite p-groups of nilpotency class 2
The origin of pairing based cryptosystems is in the MOV attack [10] on the elliptic curve discrete logarithm problem. The attack was first envisioned by Gerhard Frey. The idea was to use the bilinear properties of the Weil pairing to reduce a discrete logarithm problem in an elliptic curve over a finite field Fq to a discrete logarithm problem in Fqk . It is known [1] that most of the time for ...
متن کاملTWO GENERATOR p-GROUPS OF NILPOTENCY CLASS 2 AND THEIR CONJUGACY CLASSES
We give a classification of two-generator p-groups of nilpotency class 2. Using this classification, we give a formula for the number of such groups of order p in terms of the partitions of n of length 3, and find formulas for the number and size of their conjugacy classes.
متن کاملOn the nilpotency class of the automorphism group of some finite p-groups
Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.
متن کاملOn rational groups with Sylow 2-subgroups of nilpotency class at most 2
A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.
متن کاملProbability of having $n^{th}$-roots and n-centrality of two classes of groups
In this paper, we consider the finitely 2-generated groups $K(s,l)$ and $G_m$ as follows:$$K(s,l)=langle a,b|ab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ and find the explicit formulas for the probability of having nth-roots for them. Also, we investigate integers n for which, these groups are n-central.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 3 شماره 2
صفحات 61- 71
تاریخ انتشار 2015-12-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023