Geodesic
Maximal subgroup growth of a~few polycyclic groups
Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 226-235

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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.
Keywords: maximal subgroup growth, polycyclic groups, semidirect products. 
@article{ADM_2021_32_2_a4,
     author = {A. Kelley and E. Wolfe},
     title = {Maximal subgroup growth of a~few polycyclic groups},
     journal = {Algebra and discrete mathematics},
     pages = {226--235},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a4/}
}
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A. Kelley; E. Wolfe. Maximal subgroup growth of a~few polycyclic groups. Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 226-235. http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a4/