Real periodicity theorem for division codes

2011 ◽  
Vol 83 (1) ◽  
pp. 84-89 ◽  
Author(s):  
V. P. Filimonov
Keyword(s):  
Periodicity Theorem

Plans’ Periodicity Theorem for Jacobian of Circulant Graphs

2021 ◽  
Vol 103 (3) ◽  
pp. 139-142
Author(s):  
A. D. Mednykh ◽  
I. A. Mednykh
Keyword(s):  
Circulant Graphs ◽  
Periodicity Theorem

Delooping the total Stiefel–Whitney class

1988 ◽  
Vol 103 (1) ◽  
pp. 83-87
Author(s):  
A. Kozlowski
Keyword(s):  
Loop Space ◽  
Cohomology Ring ◽  
Group Homomorphism ◽  
Double Loop ◽  
Bott Periodicity ◽  
Group Of Units ◽  
Periodicity Theorem ◽  
Whitney Class ◽  
Infinite Loop ◽  
Infinite Loop Space

Let FH(X) denote the group of units of the classical cohomology ring H(X) = Πn≥0Hn(X; Z/2) of a CW-complex X. The total Stiefel–Whitney class can be viewed as a group homomorphism where is the reduced real K-theory of X. Both and FH( ) are representable functors, with representing spaces BO and FH, and thus w can be represented by a map w: BO → FH. By the Bott periodicity theorem, BO is an infinite loop space, and by a theorem of G. Segal[9] so is FH. However, it is well known that w is not an infinite loop map; this was first shown in [10]. The purpose of this paper is to prove the following:Theorem 0·1. w: BO → FHis a loop map but not a double loop map.

scholarly journals A periodicity theorem for acylindrically hyperbolic groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Oleg Bogopolski
Keyword(s):  
Free Groups ◽  
Hyperbolic Groups ◽  
Finitely Generated ◽  
Finitely Presented Groups ◽  
Periodicity Theorem ◽  
Finitely Presented

AbstractWe generalize a well-known periodicity lemma from the case of free groups to the case of acylindrically hyperbolic groups. This generalization has been used to describe solutions of certain equations in acylindrically hyperbolic groups and to characterize verbally closed finitely generated acylindrically hyperbolic subgroups of finitely presented groups.

FINE AND WILF'S THEOREM FOR k-ABELIAN PERIODS

2013 ◽  
Vol 24 (07) ◽  
pp. 1135-1152 ◽  
Author(s):  
JUHANI KARHUMÄKI ◽  
SVETLANA PUZYNINA ◽  
ALEKSI SAARELA
Keyword(s):  
Lower Bounds ◽  
Maximal Length ◽  
Equivalence Relations ◽  
Upper And Lower Bounds ◽  
Greatest Common Divisor ◽  
Periodicity Theorem ◽  
Abelian Case

Two words u and v are k-abelian equivalent if they contain the same number of occurrences of each factor of length at most k. This leads to a hierarchy of equivalence relations on words which lie properly in between the equality and abelian equality. The goal of this paper is to analyze Fine and Wilf's periodicity theorem with respect to these equivalence relations. Fine and Wilf's theorem tells exactly how long a word with two periods p and q can be without having the greatest common divisor of p and q as a period. Recently, the same question has been studied for abelian periods. In this paper we show that for k-abelian periods the situation is similar to the abelian case: In general, there is no bound for the lengths of such words, but the values of the parameters p, q and k for which the length is bounded can be characterized. In the latter case we provide nontrivial upper and lower bounds for the maximal lengths of such words. In some cases (e.g., for k = 2) we found the maximal length precisely.

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