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YCor
YCor
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Are the non-free factors of Grushko decomposition of a finitely generated convex–cocompactconvex-cocompact (but not cocompact) subgroup of $PSLPSL$(2,\mathbb{R})$ finite?

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LSpice
LSpice
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Are the non-free factors of Grushko decomposition of a finitely generated convex-cocompactconvex–cocompact (but not cocompact) subgroup of $PSL(2,\mathbb{R})$ finite?

See Grushko decomposition theorem.

Are the non-free factors of Grushko decomposition of a finitely generated convex–cocompact (but not cocompact) subgroup of $\operatorname{PSL}(2,\mathbb{R})$ finite?

In the cocompact case it is not true, since the group is not a free group and cannot be splittedsplit into a non-trivial free product.

For convex-cocompactconvex–cocompact but not cocompact I know of particular examples with afirmativeaffirmative answer. Is it always the case?

Are the non-free factors of Grushko decomposition of a finitely generated convex-cocompact (but not cocompact) subgroup of $PSL(2,\mathbb{R})$ finite?

See Grushko decomposition theorem.

In the cocompact case it is not true, since the group is not a free group and cannot be splitted into a non-trivial free product.

For convex-cocompact but not cocompact I know of particular examples with afirmative answer. Is it always the case?

Are the non-free factors of Grushko decomposition of a finitely generated convex–cocompact (but not cocompact) subgroup of $PSL(2,\mathbb{R})$ finite?

See Grushko decomposition theorem.

Are the non-free factors of Grushko decomposition of a finitely generated convex–cocompact (but not cocompact) subgroup of $\operatorname{PSL}(2,\mathbb{R})$ finite?

In the cocompact case it is not true, since the group is not a free group and cannot be split into a non-trivial free product.

For convex–cocompact but not cocompact I know of particular examples with affirmative answer. Is it always the case?

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EGar
EGar
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Are the non-free factors of Grushko decomposition of a finitely generated convex-cocompact (but not cocompact) subgroup of $PSL(2,\mathbb{R})$ finite?

See Grushko decomposition theorem.

In the cocompact case it is not true, since the group is not a free group and cannot be splitted into a non-trivial free product.

For convex-cocompact but not cocompact I know of particular examples with afirmative answer. Is it always the case?