  We detail the rules and mathematical structure of Al-Jabar, a game invented
by the authors based on intuitive concepts of color-mixing and ideas from
abstract algebra. Game-play consists of manipulating colored game pieces; we
discuss how these colored pieces form a group structure and how this structure,
along with an operation used to combine the pieces, is used to create a game of
strategy. We also consider extensions of the game rules to other group
structures.
  Note: While this is an article for general readership originally published
online by Gathering for Gardner in honor of Martin Gardner's birthday (Oct.
2011), Al-Jabar has been played in university abstract algebra courses as a
teaching tool, as well as by game enthusiasts, since its release. Moreover, the
algebraic game structure described has sparked further work by other
mathematicians and game designers. Thus, we submit this article to the ArXiV as
a resource for educators as well as those interested in mathematical games.
