Locally homeomorphic infinite Lindelof P-groups are homeomorphic

被引：0

作者：

Tkachenko, Mikhail ^{[1
]}

机构：

[1] Univ Autonoma Metropolitana, Dept Matemat, Ave San Rafael Atlixco 186, Mexico City 09340, Mexico

来源：

TOPOLOGY AND ITS APPLICATIONS | 2024年 / 355卷

关键词：

Lindel & ouml; f P-group; Local homeomorphism; OF-game; Menger game; omega-narrowness; Strict o-boundedness; TOPOLOGICAL-GROUPS;

D O I：

10.1016/j.topol.2024.109005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the statement formulated in the title of the article. Then we apply it to show that there exists Lindel & ouml;f P-groups G and H satisfying w(G) = w(H) = |G| = |H| = aleph 1 such that G and H are not locally homeomorphic. This solves Problem 4.4.7 from the book (Arhangel'skii and Tkachenko, 2008 [1]) in the negative. Also, we present two homeomorphic complete Abelian P-groups one of which is omega-narrow and the other is not. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：7

共 50 条

[41] An infinite family of strongly real Beauville p-groups
Gul, Sukran
MONATSHEFTE FUR MATHEMATIK, 2018, 185 (04): : 663 - 675
[42] Locally Maximal Subgroups and the Normalizer Condition in p-Groups
Asar, A. O.
ADVANCES IN GROUP THEORY AND APPLICATIONS, 2023, 16 : 5 - 22
[43] ELEMENTARY ABELIAN P-GROUPS AS AUTOMORPHISM GROUPS OF INFINITE GROUPS .1.
FOURNELLE, TA
MATHEMATISCHE ZEITSCHRIFT, 1979, 167 (03) : 259 - 270
[44] On locally finite p-groups satisfying an Engel condition
Abdollahi, A
Traustason, G
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (10) : 2827 - 2836
[45] ON LOCALLY FINITE P-GROUPS AND A PROBLEM OF HALL,PHILIP
DUGAS, M
GOBEL, R
JOURNAL OF ALGEBRA, 1993, 159 (01) : 115 - 138
[46] LOCALLY CONVEX LINEAR TOPOLOGICAL-SPACES THAT ARE HOMEOMORPHIC TO THE POWERS OF THE REAL LINE
CHIGOGIDZE, A
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 113 (02) : 599 - 609
[47] LAYER-COMPACT LOCALLY NILPOTENT P-GROUPS
POLETSKIKH, VM
CHARIN, VS
DOKLADY AKADEMII NAUK SSSR, 1971, 198 (05): : 1025 - +
[48] INFINITE ABELIAN P-GROUPS AND FINITE NORMAL SUBGROUPS OF THEIR AUTOMORPHISM GROUPS
HAUSEN, J
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (01): : A90 - &
[49] p-groups of automorphisms of Abelian p-groups
Khukhro E.I.
Algebra and Logic, 2000, 39 (3) : 207 - 214
[50] LOCALLY GRADED MINIMAL NON CC-GROUPS ARE P-GROUPS
HARTLEY, B
OTAL, J
PENA, JM
ARCHIV DER MATHEMATIK, 1991, 57 (03) : 209 - 211

← 1 2 3 4 5 →