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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).

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Examples of non-discrete, cocompact subgroups

You can find many such examples among groups acting on trees. Let $T$ be a $k$-regular tree and let $G$ be the subgroup of $\operatorname{Aut}(T)$ of automorphisms stabilizing each of the 2 parts of t …
Tom De Medts's user avatar
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12 votes
1 answer
919 views

Non-isomorphic two-transitive permutation groups with isomorphic point stabilizers

The permutation groups $A = PSL(2,7)$ with its natural action on the projective line $\mathbb{P}^1(\mathbb{F}_7)$ and $B = A\Gamma L(1,8)$ with its natural action on the affine line $\mathbb{F}_8$ hav …