On a width of verbal subgroups of certain free constructions

1997 ◽  
Vol 36 (5) ◽  
pp. 288-301 ◽  
Author(s):  
V. G. Bardakov
Keyword(s):  
Free Constructions ◽  
Verbal Subgroups

Free Constructions of Profinite Groups

2000 ◽  
pp. 361-400
Author(s):  
Luis Ribes ◽  
Pavel Zalesskii
Keyword(s):  
Profinite Groups ◽  
Free Constructions

On the definability of verbal subgroups

2001 ◽  
Vol 40 (7) ◽  
pp. 525-529
Author(s):  
Françcoise Point
Keyword(s):  
Verbal Subgroups

scholarly journals Verbal subgroups of hyperbolic groups have infinite width

2014 ◽  
Vol 90 (2) ◽  
pp. 573-591 ◽  
Author(s):  
Alexei Myasnikov ◽  
Andrey Nikolaev
Keyword(s):  
Hyperbolic Groups ◽  
Verbal Subgroups

scholarly journals The palindromic width of a free product of groups

2006 ◽  
Vol 81 (2) ◽  
pp. 199-208 ◽  
Author(s):  
Valery Bardakov ◽  
Vladimir Tolstykh
Keyword(s):  
Free Product ◽  
Free Groups ◽  
Uniform Bound ◽  
Free Products ◽  
Cyclic Groups ◽  
Similar Fact ◽  
Products Of Groups ◽  
Free Product Of Groups ◽  
Verbal Subgroups ◽  
Product Of Groups

AbstractPalindromes are those reduced words of free products of groups that coincide with their reverse words. We prove that a free product of groups G has infinite palindromic width, provided that G is not the free product of two cyclic groups of order two (Theorem 2.4). This means that there is no uniform bound k such that every element of G is a product of at most k palindromes. Earlier, the similar fact was established for non-abelian free groups. The proof of Theorem 2.4 makes use of the ideas by Rhemtulla developed for the study of the widths of verbal subgroups of free products.

scholarly journals An incomplete set of shortest descriptions

2012 ◽  
Vol 77 (1) ◽  
pp. 291-307 ◽  
Author(s):  
Frank Stephan ◽  
Jason Teutsch
Keyword(s):  
Recursion Theory ◽  
Truth Table ◽  
Outstanding Problem ◽  
Free Constructions

AbstractThe truth-table degree of the set of shortest programs remains an outstanding problem in recursion theory. We examine two related sets, the set of shortest descriptions and the set of domain-random strings, and show that the truth-table degrees of these sets depend on the underlying acceptable numbering. We achieve some additional properties for the truth-table incomplete versions of these sets, namely retraceability and approximability. We give priority-free constructions of bounded truth-table chains and bounded truth-table antichains inside the truth-table complete degree by identifying an acceptable set of domain-random strings within each degree.

Verbal Subgroups of Tr(∞,K)

2013 ◽  
Vol 42 (1) ◽  
pp. 73-80 ◽  
Author(s):  
R. Słowik
Keyword(s):  
Verbal Subgroups

scholarly journals Hyperbolic groups and free constructions

1998 ◽  
Vol 350 (2) ◽  
pp. 571-613 ◽  
Author(s):  
O. Kharlampovich ◽  
A. Myasnikov
Keyword(s):  
Hyperbolic Groups ◽  
Free Constructions
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