Maximal subgroup growth of a few polycyclic groups

• Date: 2022
• Main Authors: Kelley, A., Wolfe, E.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: maximal subgroup growth; polycyclic groups; semidirect products; 20E07
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1506
• Journal Title: Algebra and Discrete Mathematics

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...