Search Results for ""

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

Let T be a maximal torus of a group G, then T intersects every conjugacy class of G, i.e., every element g in G is conjugate to a suitable element in T. The theorem is due to ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...

There are at least two statements known as Schur's lemma. 1. The endomorphism ring of an irreducible module is a division algebra. 2. Let V, W be irreducible (linear) ...

The unitary group U_n(q) is the set of n×n unitary matrices.

The series z=ln(e^xe^y) (1) for noncommuting variables x and y. The first few terms are z_1 = x+y (2) z_2 = 1/2(xy-yx) (3) z_3 = 1/(12)(x^2y+xy^2-2xyx+y^2x+yx^2-2yxy) (4) z_4 ...

A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

Let the circles c_2 and c_3^' used in the construction of the Brocard points which are tangent to A_2A_3 at A_2 and A_3, respectively, meet again at D_A. The points D_AD_BD_C ...