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2
votes
0answers
139 views

Finitely generated subgroups are cyclic, and a generalization

Is there a name for groups $G$ which satisfy the property that for any $a$ and $b$ in $G$, there is a $c\in G$ and integers $n$ and $m$ such that $a=c^n$ and $b=c^m$? Such a group has to be abelian, ...
7
votes
1answer
266 views

What kind of category is a cyclically ordered set?

Background: A preorder is a binary relation $\leq$ which is reflexive and transitive. We can write the transitive property as ${\leq}(a,b)\wedge{\leq}(b,c)\to{\leq}(a,c)$. There are additional axioms ...
4
votes
2answers
244 views

Cyclically symmetric functions

Where can I learn about the invariant theory associated with actions of cyclic groups (as opposed to symmetric groups)? E.g., do the functions $x+y+z$, $xy+yz+zx$, and $x^2y+y^2z+z^2x$ generate the ...
2
votes
1answer
235 views

Fibered products of cyclic groups

Background Let $m,n$ be positive integers and consider the cyclic group $\mathbb{Z}_{mn}$. We have a natural epimorphism $\mathbb{Z}_{mn} \to \mathbb{Z}_n$ coming from the exact sequence $$ 0 \to ...
4
votes
1answer
262 views

Homotopy colimits of cyclic spaces

Let $\Lambda$ denote Connes's cyclic category. It is an extension of the simplex category $\Delta$ (of nonempty finite linearly ordered sets) obtained by adding an automorphism of order $n+1$ to the ...
9
votes
1answer
603 views

Cyclic spaces and S^1-equivariant homotopy theory

I'm trying to understand the relationship between cyclic spaces and S1-equivariant homotopy theory. More precisely, I only care about S1-spaces up to equivalence of fixed point spaces for the finite ...