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 infinitely...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2021 |
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| 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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| 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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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Maximal subgroup growth of a few polycyclic groups |
| spellingShingle |
Maximal subgroup growth of a few polycyclic groups Kelley, A. Wolfe, E. |
| title_short |
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_sort |
maximal subgroup growth of a few polycyclic groups |
| author |
Kelley, A. Wolfe, E. |
| author_facet |
Kelley, A. Wolfe, E. |
| publishDate |
2021 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
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Інститут прикладної математики і механіки НАН України |
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Article |
| 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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188749 |
| 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. |
| work_keys_str_mv |
AT kelleya maximalsubgroupgrowthofafewpolycyclicgroups AT wolfee maximalsubgroupgrowthofafewpolycyclicgroups |
| first_indexed |
2025-11-30T16:16:16Z |
| last_indexed |
2025-11-30T16:16:16Z |
| _version_ |
1850858122476781568 |