# Questions tagged [cyclic-groups]

Questions about the branch of algebra that deals with cyclic groups.

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### A question on a possible cyclic sieving phenomenon?

(This is an old MSE question from me, which did not get any answer, and when looking back seems interesting to post it here:) Let $G$ be a finite group. Consider the set $X_G:=\cup_{H\le G} G/H$, ...
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Define the functions $t_k(x) = \sum_{n=0}^{\infty}{\frac{x^{3n+k}}{(3n+k)!}}$ for $k=0,1,2$. The functions then satisfy: $\begin{pmatrix}\exp(x) \\ \exp(\omega x) \\ \exp(\omega^2 x)\end{pmatrix} = \... 2 votes 0 answers 53 views ### The number of elements with order less than$k$in a larger cyclic group I am working on a problem where it has become important to count (or at least bound from above and below) the number of elements of${\bf Z}/n{\bf Z}$that have order less than a given$k$, where$2\...
Let $R$ by a commutative ring with $1$, and $I \subset R$ a non-zero integral ideal in $R$. When $R$ has finite quotients, and $I = P$ is prime in $R$, the group of units $(R/P)^{\times}$ of the ...