Balanced and functionally balanced P-groups
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 topo...
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De Gruyter
2018-03-01
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| Series: | Topological Algebra and its Applications |
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| Online Access: | https://doi.org/10.1515/taa-2018-0006 |
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doaj-848e6ef994ff401e9221c2fa63d7bef02021-10-02T19:16:06ZengDe GruyterTopological Algebra and its Applications2299-32312018-03-0161535910.1515/taa-2018-0006taa-2018-0006Balanced and functionally balanced P-groupsShlossberg Menachem0Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, ItalyIn 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.https://doi.org/10.1515/taa-2018-0006itzkowitz’s problemp-groupbalanced group(strongly) functionally balanced group54e1522a05 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shlossberg Menachem |
| spellingShingle |
Shlossberg Menachem Balanced and functionally balanced P-groups Topological Algebra and its Applications itzkowitz’s problem p-group balanced group (strongly) functionally balanced group 54e15 22a05 |
| author_facet |
Shlossberg Menachem |
| author_sort |
Shlossberg Menachem |
| title |
Balanced and functionally balanced P-groups |
| title_short |
Balanced and functionally balanced P-groups |
| title_full |
Balanced and functionally balanced P-groups |
| title_fullStr |
Balanced and functionally balanced P-groups |
| title_full_unstemmed |
Balanced and functionally balanced P-groups |
| title_sort |
balanced and functionally balanced p-groups |
| publisher |
De Gruyter |
| series |
Topological Algebra and its Applications |
| issn |
2299-3231 |
| publishDate |
2018-03-01 |
| description |
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. |
| topic |
itzkowitz’s problem p-group balanced group (strongly) functionally balanced group 54e15 22a05 |
| url |
https://doi.org/10.1515/taa-2018-0006 |
| work_keys_str_mv |
AT shlossbergmenachem balancedandfunctionallybalancedpgroups |
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1716847522658385920 |