Covers and Normal Covers of Finite Groups

For a finite non cyclic group $G$, let $\gamma(G)$ be the smallest integer $k$ such that $G$ contains $k$ proper subgroups $H_1,\dots,H_k$ with the property that every element of $G$ is contained in $H_i^g$ for some $i \in \{1,\dots,k\}$ and $g \in G.$ We prove that if $G$ is a noncyclic permutation group of degree $n,$ then $\gamma(G)\leq (n+2)/2.$ We then investigate the structure of the groups $G$ with $\gamma(G)=\sigma(G)$ (where $\sigma(G)$ is the size of a minimal cover of $G$) and of those with $\gamma(G)=2.

Judging Covers

Cover versions form a loose but identifiable category of tracks and performances. We distinguish four kinds of covers and argue that they mark important differences in the modes of evaluation that are possible or appropriate for each: mimic covers, which aim merely to echo the canonical track; rendition covers, which change the sound of the canonical track; transformative covers, which diverge so much as to instantiate a distinct, albeit derivative song; and referential covers, which not only instantiate a distinct song, but for which the new song is in part about the original song. In order to allow for the very possibility of transformative and referential covers, we argue that a cover is characterized by relation to a canonical track rather than merely by being a new instance of a song that had been recorded previousl

Dylan\u27s Covers

This article discusses songs performed by musician Bob Dylan which were cover versions of songs by other performers as well as songs by Dylan which were heavily based on other songs. Songs discussed include Blowin\u27 in the Wind, which is based on the spiritual No More Auction Block, Blood in My Eyes by the band Mississippi Sheiks and When the Deal Goes Down, based on a radio theme song by musician Bing Crosby. Other topics include concerts by Dylan, music lyrics, and music performance

Cycles of Covers.

We initially consider an example of Flynn and Redmond, which gives an infinite family of curves to which Chabauty's Theorem is not applicable, and which even resist solution by one application of a certain bielliptic covering technique. In this article, we shall consider a general context, of which this family is a special case, and in this general situation we shall prove that repeated application of bielliptic covers always results in a sequence of genus 2 curves which cycle after a finite number of repetitions. We shall also give an example which is resistant to repeated applications of the technique