Common transversals and complements in abelian groups
Given a finite abelian group G and cyclic subgroups A , B , C of G of the same order, we find necessary and sufficient conditions for A , B , C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a co...
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| Veröffentlicht in: | Journal of algebraic combinatorics 2024-05, Vol.59 (3), p.581-595 |
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| container_end_page | 595 |
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| container_issue | 3 |
| container_start_page | 581 |
| container_title | Journal of algebraic combinatorics |
| container_volume | 59 |
| creator | Aivazidis, S. Loukaki, M. Sambale, B. |
| description | Given a finite abelian group
G
and cyclic subgroups
A
,
B
,
C
of
G
of the same order, we find necessary and sufficient conditions for
A
,
B
,
C
to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions. |
| doi_str_mv | 10.1007/s10801-024-01299-x |
| format | Article |
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G
and cyclic subgroups
A
,
B
,
C
of
G
of the same order, we find necessary and sufficient conditions for
A
,
B
,
C
to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.</description><identifier>ISSN: 0925-9899</identifier><identifier>EISSN: 1572-9192</identifier><identifier>DOI: 10.1007/s10801-024-01299-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Computer Science ; Convex and Discrete Geometry ; Group theory ; Group Theory and Generalizations ; Lattices ; Mathematics ; Mathematics and Statistics ; Order ; Ordered Algebraic Structures ; Subgroups</subject><ispartof>Journal of algebraic combinatorics, 2024-05, Vol.59 (3), p.581-595</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-43f7d98b5c0264d0aee9a08b4626f4199ca303347f7f40db947550ce159bc1023</cites><orcidid>0000-0002-3109-5829</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10801-024-01299-x$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10801-024-01299-x$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Aivazidis, S.</creatorcontrib><creatorcontrib>Loukaki, M.</creatorcontrib><creatorcontrib>Sambale, B.</creatorcontrib><title>Common transversals and complements in abelian groups</title><title>Journal of algebraic combinatorics</title><addtitle>J Algebr Comb</addtitle><description>Given a finite abelian group
G
and cyclic subgroups
A
,
B
,
C
of
G
of the same order, we find necessary and sufficient conditions for
A
,
B
,
C
to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.</description><subject>Combinatorics</subject><subject>Computer Science</subject><subject>Convex and Discrete Geometry</subject><subject>Group theory</subject><subject>Group Theory and Generalizations</subject><subject>Lattices</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Order</subject><subject>Ordered Algebraic Structures</subject><subject>Subgroups</subject><issn>0925-9899</issn><issn>1572-9192</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kEtLxDAURoMoOI7-AVcF19F782h7lzL4AsGNrkPapsMM06QmHRn_vdEK7lzdzTnfhcPYJcI1AlQ3CaEG5CAUBxRE_HDEFqgrwQlJHLMFkNCcaqJTdpbSFgCoRr1gehWGIfhiitanDxeT3aXC-q5owzDu3OD8lIqNL2zjdhvri3UM-zGds5M-g-7i9y7Z2_3d6-qRP788PK1un3krUU1cyb7qqG50C6JUHVjnyELdqFKUvUKi1kqQUlV91SvoGlKV1tA61NS0CEIu2dW8O8bwvndpMtuwjz6_NFnUKEulZKbETLUxpBRdb8a4GWz8NAjmO4-Z85icx_zkMYcsyVlKGfZrF_-m_7G-AORGZ30</recordid><startdate>20240501</startdate><enddate>20240501</enddate><creator>Aivazidis, S.</creator><creator>Loukaki, M.</creator><creator>Sambale, B.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3109-5829</orcidid></search><sort><creationdate>20240501</creationdate><title>Common transversals and complements in abelian groups</title><author>Aivazidis, S. ; Loukaki, M. ; Sambale, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-43f7d98b5c0264d0aee9a08b4626f4199ca303347f7f40db947550ce159bc1023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Combinatorics</topic><topic>Computer Science</topic><topic>Convex and Discrete Geometry</topic><topic>Group theory</topic><topic>Group Theory and Generalizations</topic><topic>Lattices</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Order</topic><topic>Ordered Algebraic Structures</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aivazidis, S.</creatorcontrib><creatorcontrib>Loukaki, M.</creatorcontrib><creatorcontrib>Sambale, B.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Journal of algebraic combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aivazidis, S.</au><au>Loukaki, M.</au><au>Sambale, B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Common transversals and complements in abelian groups</atitle><jtitle>Journal of algebraic combinatorics</jtitle><stitle>J Algebr Comb</stitle><date>2024-05-01</date><risdate>2024</risdate><volume>59</volume><issue>3</issue><spage>581</spage><epage>595</epage><pages>581-595</pages><issn>0925-9899</issn><eissn>1572-9192</eissn><abstract>Given a finite abelian group
G
and cyclic subgroups
A
,
B
,
C
of
G
of the same order, we find necessary and sufficient conditions for
A
,
B
,
C
to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10801-024-01299-x</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0002-3109-5829</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0925-9899 |
| ispartof | Journal of algebraic combinatorics, 2024-05, Vol.59 (3), p.581-595 |
| issn | 0925-9899 1572-9192 |
| language | eng |
| recordid | cdi_proquest_journals_3035136443 |
| source | SpringerLink Journals (MCLS) |
| subjects | Combinatorics Computer Science Convex and Discrete Geometry Group theory Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Subgroups |
| title | Common transversals and complements in abelian groups |
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