COMPUTATIONAL RESULTS ON FINITE P-GROUPS OF EXPONENT P2
Authors
Abstract:
The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. This completes the study of Fibonacci length of all $p$-groups of order p4, proving that the Fibonacci length is k(p2).
similar resources
On the Exponent of Triple Tensor Product of p-Groups
The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...
full textTHE NILPOTENCY CLASS OF FINITE GROUPS OF EXPONENT p
We investigate the properties of Lie algebras of characteristic p which satisfy the Engel identity xy" = 0 for some n < p. We establish a criterion which (when satisfied) implies that if a and b are elements of an Engel-n Lie algebra L then abn~2 generates a nilpotent ideal of I. We show that this criterion is satisfied for n = 6, p = 1, and we deduce that if G is a finite m-generator group of ...
full textSome numerical results on two classes of finite groups
In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...
full textFINITE NONABELIAN p-GROUPS OF EXPONENT > p WITH A SMALL NUMBER OF MAXIMAL ABELIAN SUBGROUPS OF EXPONENT > p
Y. Berkovich has proposed to classify nonabelian finite pgroups G of exponent > p which have exactly p maximal abelian subgroups of exponent > p and this was done here in Theorem 1 for p = 2 and in Theorem 2 for p > 2. The next critical case, where G has exactly p + 1 maximal abelian subgroups of exponent > p was done only for the case
full textON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...
full textgroups of order $p^8$ and exponent $p$
we prove that for $p>7$ there are [ p^{4}+2p^{3}+20p^{2}+147p+(3p+29)gcd (p-1,3)+5gcd (p-1,4)+1246 ] groups of order $p^{8}$ with exponent $p$. if $p$ is a group of order $p^{8}$ and exponent $p$, and if $p$ has class $c>1$ then $p$ is a descendant of $p/gamma _{c}(p)$. for each group of exponent $p$ with order less than $p^{8} $ we calculate the number of descendants of o...
full textMy Resources
Journal title
volume 2 issue 2 (SPRING)
pages 111- 120
publication date 2016-03-20
By following a journal you will be notified via email when a new issue of this journal is published.
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023