Group theory, a cornerstone of modern algebra, provides a framework to explore the structure, symmetry, and internal operations of sets endowed with a binary operation. Central to this discipline is ...

This story is a supplement to the feature "Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups"" which was printed in the July 2008 issue of Scientific American. All three new puzzles ...

We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with $\operatorname{rank}(M) > 1$, not isometric to a compact Lie group.

We give an explicit construction for the isomorphism A₈ ≅ GL₄(2). The involutions of cycle type 2³ in the symmetric group S₆, together with the null-set, can be given the structure of an elementary ...