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2021-03-07
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このアイテムへのリンクには次のURLをご利用ください:
https://doi.org/10.18910/24482
このアイテムへのリンクには次のURLをご利用ください:http://hdl.handle.net/11094/24482
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論文情報
タイトル
ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
著者
Bujalance, E.
Bujalance, E.
Gromadzki, G.
Gromadzki, G.
抄録
It is well known that a group of automorphisms G of an unbordered Klein surface X of topological genus g ≥ 2 in the orientable case and g ≥3 otherwise has at most 84(g ") elements, where " D 1 or 2 respectively. In the middle of the fifties, Oikawa used the cardinality k of a G-invariant subset to introduce the bound |G|≤12 (g- 1) C 6k in the orientable case. Much later, T. Arakawa has generalized this result, involving s D 2 or 3 such subsets and showing in addition that the bound for s D 3 is sharp for infinitely many configurations. Here we improve the bound of Arakawa for s D 2, showing in particular that the last is never attained. In both orientable and non-orientable case, we also find bounds for arbitrary s and show their sharpness for infinitely many topological configurations. Using another well known theorem of Oikawa and the canonical Riemann double cover, we get similar results for bordered Klein surfaces.
公開者
Osaka University and Osaka City University, Departments of Mathematics
掲載誌名
Osaka Journal of Mathematics
巻
50
号
1
開始ページ
251
終了ページ
269
刊行年月
2013-03
ISSN
00306126
NCID
AA00765910
URL
http://hdl.handle.net/11094/24482
言語
英語
DOI
info:doi/10.18910/24482
カテゴリ
紀要論文 Departmental Bulletin Paper
Osaka Journal of Mathematics / Volume 50, Number 1 (2013-3)
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DCTERMS.bibliographicCitation
Osaka Journal of Mathematics.50(1) P.251-P.269
DC.title
ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
DC.creator
Bujalance, E.
Gromadzki, G.
DC.publisher
Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766
英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF
2013-03
DC.identifier" scheme="DCTERMS.URI
http://hdl.handle.net/11094/24482
DCTERMS.abstract
It is well known that a group of automorphisms G of an unbordered Klein surface X of topological genus g ≥ 2 in the orientable case and g ≥3 otherwise has at most 84(g ") elements, where " D 1 or 2 respectively. In the middle of the fifties, Oikawa used the cardinality k of a G-invariant subset to introduce the bound |G|≤12 (g- 1) C 6k in the orientable case. Much later, T. Arakawa has generalized this result, involving s D 2 or 3 such subsets and showing in addition that the bound for s D 3 is sharp for infinitely many configurations. Here we improve the bound of Arakawa for s D 2, showing in particular that the last is never attained. In both orientable and non-orientable case, we also find bounds for arbitrary s and show their sharpness for infinitely many topological configurations. Using another well known theorem of Oikawa and the canonical Riemann double cover, we get similar results for bordered Klein surfaces.
DC.identifier
info:doi/10.18910/24482
citation_title
ON AUTOMORPHISMS OF KLEIN SURFACES WITH INVARIANT SUBSETS
citation_author
Bujalance, E.
Gromadzki, G.
citation_publisher
Osaka University and Osaka City University, Departments of Mathematics
citation_language
英語
citation_date
2013-03
citation_journal_title
Osaka Journal of Mathematics
citation_volume
50
citation_issue
1
citation_firstpage
251
citation_lastpage
269
citation_issn
00306126
citation_public_url
http://hdl.handle.net/11094/24482
citation_doi
info:doi/10.18910/24482