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- W4299722380 abstract "For each natural number $d$ we construct a $3$-generated group $H_d$, which is a subdirect product of free groups, such that the cohomological dimension of $H_d$ is $d$. Given a group $F$ and a normal subgroup $N lhd F$ we prove that any right angled Artin group containing the special HNN-extension of $F$ with respect to $N$ must also contain $F/N$. We apply this to construct, for every $d in mathbb{N}$, a $4$-generated group $G_d$, embeddable into a right angled Artin group, such that the cohomological dimension of $G_d$ is $2$ but the cohomological dimension of any right angled Artin group, containing $G_d$, is at least $d$. These examples are used to show the non-existence of certain universal right angled Artin groups. We also investigate finitely presented subgroups of direct products of limit groups. In particular we show that for every $nin mathbb{N}$ there exists $delta(n) in mathbb{N}$ such that any $n$-generated finitely presented subgroup of a direct product of finitely many free groups embeds into the $delta(n)$-th direct power of the free group of rank $2$. As another corollary we derive that any $n$-generated finitely presented residually free group embeds into the direct product of at most $delta(n)$ limit groups." @default.
- W4299722380 created "2022-10-03" @default.
- W4299722380 creator A5022894815 @default.
- W4299722380 date "2014-07-10" @default.
- W4299722380 modified "2023-09-27" @default.
- W4299722380 title "On subgroups of right angled Artin groups with few generators" @default.
- W4299722380 doi "https://doi.org/10.48550/arxiv.1407.2820" @default.
- W4299722380 hasPublicationYear "2014" @default.
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