Maximal subgroup growth of a few polycyclic groups
We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let Gk = ⟨x1, x2, . . . , xk | xixjxi⁻¹ for all i < j⟩, so Gk = ℤ⋊(ℤ⋊(ℤ⋊• • •⋊ℤ)). Then for all integers k ≥ 2, we calculate mn(Gk), the number of maximal subgroups of Gk of index n, exactly. Also, for infini...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188749 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Maximal subgroup growth of a few polycyclic groups / A. Kelley, E. Wolfe // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 226-235. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862634467772858368 |
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| author | Kelley, A. Wolfe, E. |
| author_facet | Kelley, A. Wolfe, E. |
| citation_txt | Maximal subgroup growth of a few polycyclic groups / A. Kelley, E. Wolfe // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 226-235. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let Gk = ⟨x1, x2, . . . , xk | xixjxi⁻¹ for all i < j⟩, so Gk = ℤ⋊(ℤ⋊(ℤ⋊• • •⋊ℤ)). Then for all integers k ≥ 2, we calculate mn(Gk), the number of maximal subgroups of Gk of index n, exactly. Also, for infinitely many groups Hk of the form ℤ² ⋊ G₂, we calculate mn(Hk) exactly.
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| first_indexed | 2025-11-30T16:16:16Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188749 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T16:16:16Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kelley, A. Wolfe, E. 2023-03-14T16:56:22Z 2023-03-14T16:56:22Z 2021 Maximal subgroup growth of a few polycyclic groups / A. Kelley, E. Wolfe // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 226-235. — Бібліогр.: 9 назв. — англ. 1726-3255 DOI:10.12958/adm1506 2020 MSC: 20E07. https://nasplib.isofts.kiev.ua/handle/123456789/188749 We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let Gk = ⟨x1, x2, . . . , xk | xixjxi⁻¹ for all i < j⟩, so Gk = ℤ⋊(ℤ⋊(ℤ⋊• • •⋊ℤ)). Then for all integers k ≥ 2, we calculate mn(Gk), the number of maximal subgroups of Gk of index n, exactly. Also, for infinitely many groups Hk of the form ℤ² ⋊ G₂, we calculate mn(Hk) exactly. This paper was done with the support of the Student Collaborative Research grant at Colorado College. We would like to thank the referee for a detailed referee report that helped us improve this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Maximal subgroup growth of a few polycyclic groups Article published earlier |
| spellingShingle | Maximal subgroup growth of a few polycyclic groups Kelley, A. Wolfe, E. |
| title | Maximal subgroup growth of a few polycyclic groups |
| title_full | Maximal subgroup growth of a few polycyclic groups |
| title_fullStr | Maximal subgroup growth of a few polycyclic groups |
| title_full_unstemmed | Maximal subgroup growth of a few polycyclic groups |
| title_short | Maximal subgroup growth of a few polycyclic groups |
| title_sort | maximal subgroup growth of a few polycyclic groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188749 |
| work_keys_str_mv | AT kelleya maximalsubgroupgrowthofafewpolycyclicgroups AT wolfee maximalsubgroupgrowthofafewpolycyclicgroups |