Balanced and functionally balanced P-groups

Menachem Shlossberg

doi:10.1515/taa-2018-0006

Balanced and functionally balanced P-groups

Menachem Shlossberg

University of Udine

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In relation to Itzkowitz's problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced. We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.

Original language	English
Pages (from-to)	53-59
Number of pages	7
Journal	Topological Algebra and its Applications
Volume	6
Issue number	1
DOIs	https://doi.org/10.1515/taa-2018-0006
State	Published - 1 Mar 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 Menachem Shlossberg, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License.

Keywords

(strongly) functionally balanced group
Balanced group
Itzkowitz's problem
P-group

Access to Document

10.1515/taa-2018-0006

Cite this

@article{870e03665cac4ddfaae6ca179a4072e0,

title = "Balanced and functionally balanced P-groups",

abstract = "In relation to Itzkowitz's problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced. We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.",

keywords = "(strongly) functionally balanced group, Balanced group, Itzkowitz's problem, P-group",

author = "Menachem Shlossberg",

note = "Publisher Copyright: {\textcopyright} 2018 Menachem Shlossberg, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License.",

year = "2018",

month = mar,

day = "1",

doi = "10.1515/taa-2018-0006",

language = "אנגלית",

volume = "6",

pages = "53--59",

journal = "Topological Algebra and its Applications",

issn = "2299-3231",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Balanced and functionally balanced P-groups

AU - Shlossberg, Menachem

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In relation to Itzkowitz's problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced. We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.

AB - In relation to Itzkowitz's problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced. We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.

KW - (strongly) functionally balanced group

KW - Balanced group

KW - Itzkowitz's problem

KW - P-group

UR - http://www.scopus.com/inward/record.url?scp=85074033407&partnerID=8YFLogxK

U2 - 10.1515/taa-2018-0006

DO - 10.1515/taa-2018-0006

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85074033407

SN - 2299-3231

VL - 6

SP - 53

EP - 59

JO - Topological Algebra and its Applications

JF - Topological Algebra and its Applications

IS - 1

ER -

Balanced and functionally balanced P-groups

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this