An infinite compact Hausdorff group has uncountably many conjugacy classes

Jaikin–Zapirain, Andrei; Nikolov, Nikolay

doi:10.1090/proc/14507

Cited by 4 publications

(4 citation statements)

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“…Thus a profinite group G with fewer than 2 ℵ0 isomorphism classes of infinite procyclic subgroups has non-trivial p-Sylow subgroups for only finitely many primes; if G also has fewer than 2 ℵ0 conjugacy classes of p-elements for each prime p it follows from Theorems A and B, and the fact that each finite nonabelian simple group has order divisible by 3 or 5, that G is finite. Therefore we recover the result of Jaikin-Zapirain and Nikolov [7] mentioned above.…”

Section: Introductionsupporting

confidence: 86%

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Profinite groupos with few conjugacy classes of $p$-elements

Wilson¹

2022

Preprint

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Section: Introductionsupporting

confidence: 86%

“…In [7], Jaikin-Zapirain and Nikolov proved that if G is a profinite group with countably many conjugacy classes then G is finite. A small extension of their argument shows that if G has fewer than 2 ℵ0 conjugacy classes then G is finite.…”

Section: Introductionmentioning

confidence: 99%

Profinite groupos with few conjugacy classes of $p$-elements

Wilson¹

2022

Preprint

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“…In [4], Jaikin-Zapirain and Nikolov proved that a profinite group with countably many conjugacy classes must be finite. A well-known theorem of Zelmanov [9] asserts that profinite torsion groups are locally finite; that is, their finite subsets generate finite subgroups.…”

Section: Introductionmentioning

confidence: 99%

Profinite groups with few conjugacy classes of 𝑝-elements

Wilson

2022

Proc. Amer. Math. Soc.

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It is proved that a profinite group G G has fewer than 2 ℵ 0 2^{\aleph _0} conjugacy classes of p p -elements for an odd prime p p if and only if its p p -Sylow p p -subgroups are finite. (Here, by a p p -element one understands an element that either has p p -power order or topologically generates a group isomorphic to Z p \mathbb {Z}_p .) A weaker result is proved for p = 2 p=2 .

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“…2.3.1]. Mas também pode-se provar que o conjunto das classes de conjugação de um grupo profinito infinito é sempre não-enumerável [JN19].…”

Section: áLgebras De Grupos Profinitosunclassified

Homologia de álgebras pseudocompactas: as fronteiras da conjectura de Han

Cruz¹

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To know you couldn't have gotten there on your own? Wouldn't it be nice, if you loseTo value a choir to sing the blues, with you?-Erlend Øye & Eirik Glambek Bøe À minha mãe e ao meu pai, por terem me fornecido minha educação basilar, a qual me é impossível mensurar sua importância.Ao Guilherme e ao Heitor, pela companhia nos caminhos da graduação.Ao André, por me mostrar a importância da história nas ciências.Ao Kostia, por nos estimular à troca de ideias, seja em nosso pequeno seminário online durante a quarentena, em nossas reuniões híbridas durante seu período na Ucrânia ou na organização de seminários no IME.Ao Roger e ao Mateus, por todas as reuniões.Enfim, a todos agradeço pelas conversas. ResumoGuilherme da Costa Cruz. Homologia de Álgebras Pseudocompactas: as fronteiras da conjectura de Han. Dissertação (Mestrado).

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An infinite compact Hausdorff group has uncountably many conjugacy classes

Abstract: We show that an infinite compact Hausdorff group has uncountably many conjugacy classes.

Cited by 4 publications

References 11 publications

Profinite groupos with few conjugacy classes of $p$-elements

Profinite groupos with few conjugacy classes of $p$-elements

Profinite groups with few conjugacy classes of 𝑝-elements

Homologia de álgebras pseudocompactas: as fronteiras da conjectura de Han

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