A New Characterization of PSL(2, q) for Some q
Let G be a finite group and let π e (G) be the set of orders of elements from G. Let k ∈ π e (G) and let m k be the number of elements of order k in G. We set nse (G) := {m k | k ∈ π e (G)}. It is proved that PSL(2, q) are uniquely determined by nse (PSL(2, q)), where q ∈ {5, 7, 8, 9, 11, 13}. As th...
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| Published in: | Український математичний журнал |
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| Date: | 2015 |
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| Cite this: | A New Characterization of PSL(2, q) for Some q / A.K. Asboei, S.S.S. Amiri, A. Iranmanesh // Український математичний журнал. — 2015. — Т. 67, № 9. — С. 1155–1162. — Бібліогр.: 14 назв. — англ. |
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Asboei, A.K. Amiri, S.S.S. Iranmanesh, A. 2020-02-16T20:30:45Z 2020-02-16T20:30:45Z 2015 A New Characterization of PSL(2, q) for Some q / A.K. Asboei, S.S.S. Amiri, A. Iranmanesh // Український математичний журнал. — 2015. — Т. 67, № 9. — С. 1155–1162. — Бібліогр.: 14 назв. — англ. 1027-3190 https://nasplib.isofts.kiev.ua/handle/123456789/165855 512.5 Let G be a finite group and let π e (G) be the set of orders of elements from G. Let k ∈ π e (G) and let m k be the number of elements of order k in G. We set nse (G) := {m k | k ∈ π e (G)}. It is proved that PSL(2, q) are uniquely determined by nse (PSL(2, q)), where q ∈ {5, 7, 8, 9, 11, 13}. As the main result of the paper, we prove that if G is a group such that nse (G) = nse (PSL(2, q)), where q ∈ {16, 17, 19, 23}, then G ≅ PSL(2, q). Нехай G — скінченна група, а πe(G) — множина порядків елемента з G. Нехай також k∈πe(G), а mk — число елементів порядку k в G. Покладемо nse (G):={mk|k∈πe(G)}. Доведено, що PSL(2,q) однозначно визначаються nse (PSL(2,q)), де q∈{5,7,8,9,11,13}. Основним результатом роботи є доведення того факту, що якщо G є групою, для якої nse (G)=nse(PSL(2,q)), де q∈16,17,19,23, то G≅PSL(2,q). Partial support by the Center of Excellence of Algebraic Hyper structures and its Applications of Tarbiat Modares University (CEAHA) is gratefully acknowledge by the third author en Інститут математики НАН України Український математичний журнал Статті A New Characterization of PSL(2, q) for Some q Нова характеристика PSL(2,q) для деякого q Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
A New Characterization of PSL(2, q) for Some q |
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A New Characterization of PSL(2, q) for Some q Asboei, A.K. Amiri, S.S.S. Iranmanesh, A. Статті |
| title_short |
A New Characterization of PSL(2, q) for Some q |
| title_full |
A New Characterization of PSL(2, q) for Some q |
| title_fullStr |
A New Characterization of PSL(2, q) for Some q |
| title_full_unstemmed |
A New Characterization of PSL(2, q) for Some q |
| title_sort |
new characterization of psl(2, q) for some q |
| author |
Asboei, A.K. Amiri, S.S.S. Iranmanesh, A. |
| author_facet |
Asboei, A.K. Amiri, S.S.S. Iranmanesh, A. |
| topic |
Статті |
| topic_facet |
Статті |
| publishDate |
2015 |
| language |
English |
| container_title |
Український математичний журнал |
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Інститут математики НАН України |
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Article |
| title_alt |
Нова характеристика PSL(2,q) для деякого q |
| description |
Let G be a finite group and let π e (G) be the set of orders of elements from G. Let k ∈ π e (G) and let m k be the number of elements of order k in G. We set nse (G) := {m k | k ∈ π e (G)}. It is proved that PSL(2, q) are uniquely determined by nse (PSL(2, q)), where q ∈ {5, 7, 8, 9, 11, 13}. As the main result of the paper, we prove that if G is a group such that nse (G) = nse (PSL(2, q)), where q ∈ {16, 17, 19, 23}, then G ≅ PSL(2, q).
Нехай G — скінченна група, а πe(G) — множина порядків елемента з G. Нехай також k∈πe(G), а mk — число елементів порядку k в G. Покладемо nse (G):={mk|k∈πe(G)}. Доведено, що PSL(2,q) однозначно визначаються nse (PSL(2,q)), де q∈{5,7,8,9,11,13}. Основним результатом роботи є доведення того факту, що якщо G є групою, для якої nse (G)=nse(PSL(2,q)), де q∈16,17,19,23, то G≅PSL(2,q).
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| issn |
1027-3190 |
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https://nasplib.isofts.kiev.ua/handle/123456789/165855 |
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| citation_txt |
A New Characterization of PSL(2, q) for Some q / A.K. Asboei, S.S.S. Amiri, A. Iranmanesh // Український математичний журнал. — 2015. — Т. 67, № 9. — С. 1155–1162. — Бібліогр.: 14 назв. — англ. |
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2025-11-24T04:54:02Z |
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