scholarly journals Compact groups containing dense pseudocompact subgroups without non-trivial convergent sequences

2007 ◽  
Vol 154 (2) ◽  
pp. 476-490 ◽  
Author(s):  
J. Galindo ◽  
S. Garcia-Ferreira
Keyword(s):  
Compact Groups ◽  
Convergent Sequences

scholarly journals Countably compact groups without non-trivial convergent sequences

2020 ◽  
Vol 374 (2) ◽  
pp. 1277-1296 ◽  
Author(s):  
M. Hrušák ◽  
J. van Mill ◽  
U. A. Ramos-García ◽  
S. Shelah
Keyword(s):  
Compact Groups ◽  
Countably Compact ◽  
Convergent Sequences

Some classes of ideal convergent sequences and generalized difference matrix operator

Filomat ◽  
2017 ◽  
Vol 31 (6) ◽  
pp. 1827-1834 ◽  
Author(s):  
S.A. Mohiuddine ◽  
B. Hazarika
Keyword(s):  
Matrix Operator ◽  
Difference Matrix ◽  
Convergent Sequences

scholarly journals Compact groups with a set of positive Haar measure satisfying a nilpotent law

2021 ◽  
pp. 1-4
Author(s):  
ALIREZA ABDOLLAHI ◽  
MEISAM SOLEIMANI MALEKAN
Keyword(s):  
Compact Group ◽  
Haar Measure ◽  
Positive Answer ◽  
Nilpotent Subgroup ◽  
Compact Groups

Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .

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