Maximal subgroup growth of a few polycyclic groups

• Published in: Algebra and Discrete Mathematics
• Date: 2021
• Main Authors: Kelley, A., Wolfe, E.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188749
• 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.

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...