Minimal non-\(PC\)-groups
The purpose of this paper is to prove that a non-perfect group \(G\) is a minimal non-\(PC\)-group if and only if it is a minimal non-\(FC\)-group. It is shown that a perfect locally graded minimal non-\(PC\)-group is an indecomposable countable locally finite \(p\)-group.
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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1041 |
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-10412018-04-26T02:28:53Z Minimal non-\(PC\)-groups Artemovych, Orest D. \(PC\)-group, \(FC\)-group 20F24, 20E45 The purpose of this paper is to prove that a non-perfect group \(G\) is a minimal non-\(PC\)-group if and only if it is a minimal non-\(FC\)-group. It is shown that a perfect locally graded minimal non-\(PC\)-group is an indecomposable countable locally finite \(p\)-group. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1041 Algebra and Discrete Mathematics; Vol 18, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1041/563 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
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| datestamp_date |
2018-04-26T02:28:53Z |
| collection |
OJS |
| language |
English |
| topic |
\(PC\)-group \(FC\)-group 20F24 20E45 |
| spellingShingle |
\(PC\)-group \(FC\)-group 20F24 20E45 Artemovych, Orest D. Minimal non-\(PC\)-groups |
| topic_facet |
\(PC\)-group \(FC\)-group 20F24 20E45 |
| format |
Article |
| author |
Artemovych, Orest D. |
| author_facet |
Artemovych, Orest D. |
| author_sort |
Artemovych, Orest D. |
| title |
Minimal non-\(PC\)-groups |
| title_short |
Minimal non-\(PC\)-groups |
| title_full |
Minimal non-\(PC\)-groups |
| title_fullStr |
Minimal non-\(PC\)-groups |
| title_full_unstemmed |
Minimal non-\(PC\)-groups |
| title_sort |
minimal non-\(pc\)-groups |
| description |
The purpose of this paper is to prove that a non-perfect group \(G\) is a minimal non-\(PC\)-group if and only if it is a minimal non-\(FC\)-group. It is shown that a perfect locally graded minimal non-\(PC\)-group is an indecomposable countable locally finite \(p\)-group. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1041 |
| work_keys_str_mv |
AT artemovychorestd minimalnonpcgroups |
| first_indexed |
2025-12-02T15:24:42Z |
| last_indexed |
2025-12-02T15:24:42Z |
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1850411827069976576 |