منابع مشابه
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...
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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. Th...
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We consider the capability of p-groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition based on the ranks of G/Z(G) and [G, G].
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Let E be an elliptic curve defined over Fq, the finite field of q elements. We show that for some constant η > 0 depending only on q, there are infinitely many positive integers n such that the exponent of E(Fqn), the group of Fqn-rational points on E, is at most q exp ( −n log logn ) . This is an analogue of a result of R. Schoof on the exponent of the group E(Fp) of Fp-rational points, when a...
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In [GrH97], Grigorchuk and de la Harpe ask for conditions under which some group presentations have growth rate close to that of the free group with the same number of generators. We prove that this property holds for a generic group (in the density model of random groups). Namely, for every positive ε, the property of having growth exponent at least 1 − ε (in base 2m − 1 where m is the number ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1972-0289631-2