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- W3133663301 abstract "A $vee$-complement of a subgroup $H leqslant mathbb{F}_n$ is a subgroup $K leqslant mathbb{F}_n$ such that $H vee K = mathbb{F}_n$. If we also ask $K$ to have trivial intersection with $H$, then we say that $K$ is a $oplus$-complement of $H$. The minimum possible rank of a $vee$-complement (resp. $oplus$-complement) of $H$ is called the $vee$-corank (resp. $oplus$-corank) of $H$. We use Stallings automata to study these notions and the relations between them. In particular, we characterize when complements exist, compute the $vee$-corank, and provide language-theoretical descriptions of the sets of cyclic complements. Finally, we prove that the two notions of corank coincide on subgroups that admit cyclic complements of both kinds." @default.
- W3133663301 created "2021-03-15" @default.
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- W3133663301 date "2020-03-02" @default.
- W3133663301 modified "2023-09-25" @default.
- W3133663301 title "On the lattice of subgroups of a free group: complements and rank" @default.
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- W3133663301 doi "https://doi.org/10.46298/jgcc.2020.12.1.6059" @default.
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