The genus of the subgroup graph of a finite group
For a finite group G denote by γ(L(G)) the genus of the subgroup graph of G. We prove that γ(L(G)) tends to infinity as either the rank of G or the number of prime divisors of |G| tends to infinity.
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2021-04-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500101 |
| _version_ | 1818972471472160768 |
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| author | Andrea Lucchini |
| author_facet | Andrea Lucchini |
| author_sort | Andrea Lucchini |
| collection | DOAJ |
| description | For a finite group G denote by γ(L(G)) the genus of the subgroup graph of G. We prove that γ(L(G)) tends to infinity as either the rank of G or the number of prime divisors of |G| tends to infinity. |
| first_indexed | 2024-12-20T15:08:48Z |
| format | Article |
| id | doaj.art-3a70741b0bbf49ee8de5813156d1afd8 |
| institution | Directory Open Access Journal |
| issn | 1664-3607 1664-3615 |
| language | English |
| last_indexed | 2024-12-20T15:08:48Z |
| publishDate | 2021-04-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj.art-3a70741b0bbf49ee8de5813156d1afd82022-12-21T19:36:23ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152021-04-011112050010-12050010-610.1142/S166436072050010110.1142/S1664360720500101The genus of the subgroup graph of a finite groupAndrea Lucchini0Dipartimento di Matematica, “Tullio Levi-Civita”, Università di Padova, Via Trieste, 63, 35131 Padova, ItalyFor a finite group G denote by γ(L(G)) the genus of the subgroup graph of G. We prove that γ(L(G)) tends to infinity as either the rank of G or the number of prime divisors of |G| tends to infinity.http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500101finite groupsgenussubgroup graph |
| spellingShingle | Andrea Lucchini The genus of the subgroup graph of a finite group Bulletin of Mathematical Sciences finite groups genus subgroup graph |
| title | The genus of the subgroup graph of a finite group |
| title_full | The genus of the subgroup graph of a finite group |
| title_fullStr | The genus of the subgroup graph of a finite group |
| title_full_unstemmed | The genus of the subgroup graph of a finite group |
| title_short | The genus of the subgroup graph of a finite group |
| title_sort | genus of the subgroup graph of a finite group |
| topic | finite groups genus subgroup graph |
| url | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500101 |
| work_keys_str_mv | AT andrealucchini thegenusofthesubgroupgraphofafinitegroup AT andrealucchini genusofthesubgroupgraphofafinitegroup |