This is a preview. Log in through your library . Abstract Let Sym M be the symmetric group of an infinite set M. What is the smallest subgroup of Sym M containing a given element if the subgroup is ...

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.