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A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

In Note M, Burnside (1955) states, "The contrast that these results shew between groups of odd and of even order suggests inevitably that simple groups of odd order do not ...

Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

If f is a schlicht function and D(z_0,r) is the open disk of radius r centered at z_0, then f(D(0,1)) superset= D(0,1/4), where superset= denotes a (not necessarily proper) ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...