scholarly journals Cohomology of profinite groups of bounded rank

2021 ◽  
Vol 8 (1) ◽  
pp. 435-439
Author(s):  
Peter Symonds
Keyword(s):  
Profinite Groups ◽  
Bounded Rank

scholarly journals Isomorphism, canonization, and definability for graphs of bounded rank width

2021 ◽  
Vol 64 (5) ◽  
pp. 98-105
Author(s):  
Martin Grohe ◽  
Daniel Neuen
Keyword(s):  
Fixed Point ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Descriptive Complexity ◽  
Graph Isomorphism Problem ◽  
Structural Graph ◽  
Graph Classes ◽  
Bounded Rank

We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width.

Burnside algebras of profinite groups

1994 ◽  
Vol 22 (5) ◽  
pp. 1551-1575 ◽  
Author(s):  
R.S. Pierce
Keyword(s):  
Profinite Groups

scholarly journals On hereditarily just infinite profinite groups obtained via iterated wreath products

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Vannacci Matteo
Keyword(s):  
Wreath Products ◽  
Profinite Groups ◽  
The Family

AbstractWe study a generalisation of the family of non-(virtually pro-

Permutation modules of profinite groups

2017 ◽  
Vol 58 (4) ◽  
pp. 687-692
Author(s):  
K. N. Ponomarev
Keyword(s):  
Profinite Groups

scholarly journals Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width

2013 ◽  
Vol 123 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Robert Ganian ◽  
Petr Hliněný ◽  
Jan Obdržálek
Keyword(s):  
Satisfiability Problems ◽  
Bounded Rank
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