Maximal subgroup growth of a few polycyclic groups
We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let \(G_k = \langle x_1, x_2, \dots , x_k \mid x_ix_jx_i^{-1}x_j \text{ for all } i < j \rangle\), so \(G_k = \mathbb{Z} \rtimes (\mathbb{Z} \rtimes (\mathbb{Z} \rtimes \dots \rtimes \mathbb{Z}))\). Then for a...
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Lugansk National Taras Shevchenko University
2022
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oai:ojs.admjournal.luguniv.edu.ua:article-15062022-03-28T05:34:02Z Maximal subgroup growth of a few polycyclic groups Kelley, A. Wolfe, E. maximal subgroup growth, polycyclic groups, semidirect products 20E07 We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let \(G_k = \langle x_1, x_2, \dots , x_k \mid x_ix_jx_i^{-1}x_j \text{ for all } i < j \rangle\), so \(G_k = \mathbb{Z} \rtimes (\mathbb{Z} \rtimes (\mathbb{Z} \rtimes \dots \rtimes \mathbb{Z}))\). Then for all integers \(k \geq 2\), we calculate \(m_n(G_k)\), the number of maximal subgroups of \(G_k\) of index \(n\), exactly. Also, for infinitely many groups \(H_k\) of the form \(\mathbb{Z}^2 \rtimes G_2\), we calculate \(m_n(H_k)\) exactly. Lugansk National Taras Shevchenko University 2022-03-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1506 10.12958/adm1506 Algebra and Discrete Mathematics; Vol 32, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1506/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1506/626 Copyright (c) 2022 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2022-03-28T05:34:02Z |
| collection |
OJS |
| language |
English |
| topic |
maximal subgroup growth polycyclic groups semidirect products 20E07 |
| spellingShingle |
maximal subgroup growth polycyclic groups semidirect products 20E07 Kelley, A. Wolfe, E. Maximal subgroup growth of a few polycyclic groups |
| topic_facet |
maximal subgroup growth polycyclic groups semidirect products 20E07 |
| format |
Article |
| author |
Kelley, A. Wolfe, E. |
| author_facet |
Kelley, A. Wolfe, E. |
| author_sort |
Kelley, A. |
| title |
Maximal subgroup growth of a few polycyclic groups |
| 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 |
| description |
We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let \(G_k = \langle x_1, x_2, \dots , x_k \mid x_ix_jx_i^{-1}x_j \text{ for all } i < j \rangle\), so \(G_k = \mathbb{Z} \rtimes (\mathbb{Z} \rtimes (\mathbb{Z} \rtimes \dots \rtimes \mathbb{Z}))\). Then for all integers \(k \geq 2\), we calculate \(m_n(G_k)\), the number of maximal subgroups of \(G_k\) of index \(n\), exactly. Also, for infinitely many groups \(H_k\) of the form \(\mathbb{Z}^2 \rtimes G_2\), we calculate \(m_n(H_k)\) exactly. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2022 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1506 |
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AT kelleya maximalsubgroupgrowthofafewpolycyclicgroups AT wolfee maximalsubgroupgrowthofafewpolycyclicgroups |
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2025-07-17T10:32:23Z |
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2025-07-17T10:32:23Z |
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1837889847771004928 |