Every group has at least two subgroups, itself and the subgroup whose only member is (1); a proper subgroup is any other subgroup that may exist. So What Is Normal?

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 ...

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 ...

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.