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Questions about the branch of algebra that deals with groups.

2 votes
1 answer
171 views

Order of a loop around a cone point

Let $M$ be a connected orientable two-dimensional orbifold with only cone points as singular points. Assume that $M$ has genus $\geq 1$. Let $\alpha$ be a loop around an order $p$ cone point. Can we c …
RKS's user avatar
  • 585
10 votes
3 answers
552 views

Centre of orbifold fundamental group of torus (Klein bottle) with one cone point

$\newcommand{\orb}{\mathrm{orb}}$Let $T$ ($K$) be the torus (Klein bottle) with one cone point of order $q\geq 2$. The presentation of their orbifold fundamental groups are easy to find. Namely, $$\p …
RKS's user avatar
  • 585
7 votes
1 answer
285 views

Distinguishing poly-free groups

I have two discrete groups $G_1$ and $G_2$ sitting in the following exact sequences: $1\to H_1\to G_1\to K_1\to 1$ and $1\to H_2\to G_2\to K_2\to 1$. $H_1$, $K_1$, $H_2$ and $K_2$ are all non-abelian …
RKS's user avatar
  • 585