J. Schlage-Puchta

activity

20032026

most citedOn triangular billiards

38 citations · 123 across the 49 of their papers we have counts for

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11 papers · 1 filter

math.GR2025

The normal growth of linear groups over formal power serieses

Yiftach Barnea, Jan-Christoph Schlage-Puchta

Put $R=\F[[t_1, \ldots, t_d]])$. We estimate the number of normal subgroups of $\mathrm{SL}_2^1(\F[[t_1, \ldots, t_d]])$ for $p > 2$ , the number of ideals in the Lie algebra $\Lie(R)…

math.GR2019★ 1 cited

How many quasiplatonic curves?

Jan-Christoph Schlage-Puchta, Jürgen Wolfart

We show that the number of isomorphism classes of quasiplatonic Riemann surfaces of genus $\leq g$ has a growth of type $g^{l o g g}$ . The number of non--isomorphic regular d…

math.GR2017

Large normal subgroup growth and large characteristic subgroup growth

Yiftach Barnea, Jan-Christoph Schlage-Puchta

The maximal normal subgroup growth type of a finitely generated group is $n^{l o g n}$ . Very little is known about groups with this type of growth. In particular, the following is a…

math.GR2016

Branch groups, orbit growth, and subgroup growth types for pro- $p$ groups

Yiftach Barnea, Jan-Christoph Schlage-Puchta

We first show that a class of pro- $p$ branch groups including the Grigorchuk group and the Gupta-Sidki groups all have subgroup growth type $n^{l o g n}$ . We then introduce the noti…

math.GR2011★ 5 cited

On $p$ -deficiency in groups

Yiftach Barnea, Jan-Christoph Schlage-Puchta

Recently, Schlage-Puchta proved super multiplicity of $p$ -deficiency for normal subgroups of $p$ -power index. We extend this result to all normal subgroups of finite index. We then…

math.GR2011★ 2 cited

A $p$ -group with positive Rank Gradient

Jan-Christoph Schlage-Puchta

We construct for $d \geq 2$ and $ε > 0$ a $d$ -generated $p$ -group $Γ$ , which in an asymptotic sense behaves almost like a $d$ -generated free pro- $p$ -group. We show that a subgroup of…

math.GR2011

The order of elements in Sylow $p$ -subgroups of the symmetric group

Jan-Christoph Schlage-Puchta

Define a random variable $ξ_{n}$ by choosing a conjugacy class $C$ of the Sylow $p$ -subgroup of $S_{p^{n}}$ by random, and let $ξ_{n}$ be the logarithm of the order of an element in $C$ .…

math.GR2011

Sifted character sums and free quotients of Bianchi groups

Jan-Christoph Schlage-Puchta

We show that the Bianchi group $PSL_{2} (O_{d})$ , where $O_{d}$ is the ring of integers in $\Q(\sqrt{d})$, $d < 0$ , has a free quotient of rank $\geq |d|^{1/4-ε…

math.GR2011

Homomorphisms from a finite group into wreath products

Jan-Christoph Schlage-Puchta

Let $G$ be a finite group, $A$ a finite abelian group. Each homomorphism $ϕ : G \to A ≀ S_{n}$ induces a homomorphism $ϕ ˉ : G \to A$ in a natural way. We show that as $ϕ$ is chosen ran…

math.GR2011

The subgroup growth spectrum of virtually free groups

Jan-Christoph Schlage-Puchta

For a finitely generated group $Γ$ denote by $μ (Γ)$ the growth coefficient of $Γ$ , that is, the infimum over all real numbers $d$ such that $s_{n} (Γ) < n!^{d}$ . We show that the growth c…

math.GR2003★ 2 cited

Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks

Thomas W. Mueller, Jan-Christoph Schlage-Puchta

We derive an asymptotic expansion for the subgroup of arbitrary Fuchsian groups and some other classes of large groups. Moreover, the main conjecture for Random Walks on symmetric…

The normal growth of linear groups over formal power serieses

How many quasiplatonic curves?

Large normal subgroup growth and large characteristic subgroup growth

Branch groups, orbit growth, and subgroup growth types for pro-p groups

On p-deficiency in groups

A p-group with positive Rank Gradient

The order of elements in Sylow p-subgroups of the symmetric group

Sifted character sums and free quotients of Bianchi groups

Homomorphisms from a finite group into wreath products

The subgroup growth spectrum of virtually free groups

Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks

Branch groups, orbit growth, and subgroup growth types for pro- $p$ groups

On $p$ -deficiency in groups

A $p$ -group with positive Rank Gradient

The order of elements in Sylow $p$ -subgroups of the symmetric group