منابع مشابه
Two-generator Subgroups of the Pure Braid Group
We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.
متن کاملRandom Subgroups of Braid Groups: An Approach to Cryptanalysis of a Braid Group Based Cryptographic Protocol
Motivated by cryptographic applications, we study subgroups of braid groups Bn generated by a small number of random elements of relatively small lengths compared to n. Our experiments show that “most” of these subgroups are equal to the whole Bn, and “almost all” of these subgroups are generated by positive braid words. We discuss the impact of these experimental results on the security of the...
متن کاملPure Braid Subgroups of Braided Thompson’s Groups
We describe pure braided versions of Thompson’s group F . These groups, BF and B̂F , are subgroups of the braided versions of Thompson’s group V , introduced by Brin and Dehornoy. Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe i...
متن کاملSOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP
Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...
متن کاملA Practical Attack on Some Braid Group Based Cryptographic Primitives
A simple heuristic approach to the conjugacy problem in braid groups is described. Although it does not provide a general solution to the latter problem, it demonstrates that various proposed key parameters for braid group based cryptographic primitives do not offer acceptable cryptographic security. We give experimental evidence that it is often feasible to reveal the secret data by means of a...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1997
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(96)00152-6