K. Podoski

activity

20072023

most citedEvery coprime linear group admits a base of size two

18 citations · 19 across the 4 of their papers we have counts for

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5 papers · 1 filter

math.GR2023

On $p$ -groups with a maximal elementary abelian normal subgroup of rank $k$

Zoltán Halasi, Károly Podoski, László Pyber +1

There are several results in the literature concerning $p$ -groups $G$ with a maximal elementary abelian normal subgroup of rank $k$ due to Thompson, Mann and others. Following an i…

math.GR2019

Random bases for coprime linear groups

Hülya Duyan, Zoltán Halasi, Károly Podoski

The minimal base size $b (G)$ for a permutation group $G$ , is a widely studied topic in the permutation group theory. Z. Halasi and K. Podoski proved that $b (G) \leq 2$ for coprime l…

math.GR2012★ 18 cited

Every coprime linear group admits a base of size two

Zoltán Halasi, Károly Podoski

Let G be a linear group acting on the finite vector space V and assume that (|G|,|V|)=1. In this paper we prove that G has a base size at most two and this estimate is sharp. This…

math.GR2007★ 1 cited

On the Orbits of Solvable Linear Groups

Zoltan Halasi, Karoly Podoski

Let $G$ be a solvable linear group acting on the finite vectorpace $V$ and assume that $(∣ G ∣, ∣ V ∣) = 1$ . In this paper we find $x, y \in V$ such that $C_{G} (x) \cap C_{G} (y) = 1$ . In particula…

math.GR2007

On finite groups whose derived subgroup has bounded rank

Karoly Podoski, Balazs Szegedy

Let $G$ be a finite group with derived subgroup of rank $r$ . We prove that $\gzz\leq |G'|^{2r}$. Motivated by the results of I. M. Isaacs in \cite{isa} we show that if $G$ is capab…