几个多环群的极大子群增长

IF 0.3 Q4 MATHEMATICS, APPLIED Algebra & Discrete Mathematics Pub Date : 2019-11-16 DOI:10.12958/adm1506

A. J. Kelley, Elizabeth Ciorsdan Dwyer Wolfe

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引用次数: 0

摘要

本文给出了两类多环群的精确极大子群增长。LetGk=⟨x1, x2，…, xk | xixjx−1 ixjfor alli < j⟩,soGk = Z⋊(Z⋊(Z⋊···⋊Z))。然后对于所有integersk大于或等于2，我们精确地计算n(Gk)， Gk指数n的最大子组的数量。同样，对于inőnitely许多形式为Z2 * * * G2的群，我们精确地计算了n(Hk)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Maximal subgroup growth of a few polycyclic groups

We give here the exact maximal subgroup growthof two classes of polycyclic groups. LetGk=⟨x1, x2, . . . , xk|xixjx−1ixjfor alli < j⟩, soGk=Z ⋊(Z ⋊(Z ⋊· · ·⋊ Z)). Then forall integersk⩾2, we calculatemn(Gk), the number of maximalsubgroups ofGkof indexn, exactly. Also, for inőnitely many groupsHkof the form Z2⋊G2, we calculatemn(Hk)exactly.

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