Profinite groups with many commuting pairs or involutions

被引：15

作者：

Lévai, L ^{[1
]}

Pyber, L ^{[1
]}

机构：

[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary

来源：

ARCHIV DER MATHEMATIK | 2000年 / 75卷 / 01期

关键词：

D O I：

10.1007/s000130050466

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if the set of commuting pairs of a profinite group G has positive Haar measure then G is abelian by finite. Using this we show that the set I of involutions has positive measure exactly if I contains a nonempty open subset of G.

引用

页码：1 / 7

页数：7

共 14 条

[1] [Anonymous], 1896, GRUPPENCHARAKTERE SI
[2] ON THE NUMBER OF ELEMENTS WHICH ARE NOT N-TH POWERS IN FINITE-GROUPS
BANNAI, E
DEZA, M
FRANKL, P
KIM, AC
KIYOTA, M
[J]. COMMUNICATIONS IN ALGEBRA, 1989, 17 (11) : 2865 - 2870
[3] FROBENIUS G, 1903, FUNDAMENTALSATZ GRUP, P987
[4] FROBENIUS G, 1906, REELLEN DARSTELLUNGE, P186
[5] Hall P, 1936, P LOND MATH SOC, V40, P468
[6] Hamidoune Y. O., 1981, European Journal of Combinatorics, V2, P349
[7] Linear core conditions in residually finite groups
Levai, L
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1998, 105 (1) : 337 - 348
[8] GROUPS WITH AUTOMORPHISMS INVERTING MOST ELEMENTS
LIEBECK, H
MACHALE, D
[J]. MATHEMATISCHE ZEITSCHRIFT, 1972, 124 (01) : 51 - +
[9] The exponent of finite groups
Mann, A
Martinez, C
[J]. ARCHIV DER MATHEMATIK, 1996, 67 (01) : 8 - 10
[10] MEDNYH AD, 1978, SOV MATH DOKL, V19, P318

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