Gaps in probabilities of satisfying some commutator-like identities

被引:4
作者
Delizia, Costantino [1 ]
Jezernik, Urban [2 ]
Moravec, Primoz [3 ]
Nicotera, Chiara [1 ]
机构
[1] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo II 132, I-84084 Fisciano, Italy
[2] Univ Basque Country, Dept Matemat, Apartado 644, Bilbao 48080, Spain
[3] Univ Ljubljana, Fac Math & Phys, Jadranska Ulica 19, SI-1000 Ljubljana, Slovenia
基金
欧盟地平线“2020”;
关键词
D O I
10.1007/s11856-020-1999-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We show that there is a positive constant delta < 1 such that the probability of satisfying either the 2-Engel identity [X-1, X-2, X-2] = 1 or the metabelian identity [[X-1, X-2], [X-3, X-4]] = 1 in a finite group is either 1 or at most delta
引用
收藏
页码:115 / 140
页数:26
相关论文
共 13 条
[2]   Commuting probabilities of finite groups [J].
Eberhard, Sean .
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2015, 47 :796-808
[3]   On the relative commutativity degree of a subgroup of a finite group [J].
Erfanian, A. ;
Rezaei, R. ;
Lescot, P. .
COMMUNICATIONS IN ALGEBRA, 2007, 35 (12) :4183-4197
[4]   3RD ENGEL GROUPS [J].
GUPTA, ND ;
NEWMAN, MF .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1989, 40 (02) :215-230
[5]   WHAT IS PROBABILITY THAT 2 GROUP ELEMENTS COMMUTE [J].
GUSTAFSON, WH .
AMERICAN MATHEMATICAL MONTHLY, 1973, 80 (09) :1031-1034
[6]   Words, Hausdorff dimension and randomly free groups [J].
Larsen, Michael ;
Shalev, Aner .
MATHEMATISCHE ANNALEN, 2018, 371 (3-4) :1409-1427
[7]   Fibers of word maps and some applications [J].
Larsen, Michael ;
Shalev, Aner .
JOURNAL OF ALGEBRA, 2012, 354 (01) :36-48
[8]  
Martino A., PROBABILISTIC NILPOT
[9]   2 COMBINATORIAL PROBLEMS IN GROUP-THEORY [J].
NEUMANN, PM .
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1989, 21 :456-458
[10]   Verbal width in anabelian groups [J].
Nikolov, Nikolay .
ISRAEL JOURNAL OF MATHEMATICS, 2016, 216 (02) :847-876