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In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent ...

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

A finite group L is quasisimple if L=[L,L] and L/Z(L) is a simple group.

A property of finite simple groups which is known for all such groups.

The baby monster group, also known as Fischer's baby monster group, is the second-largest sporadic group. It is denoted B and has group order |B| = ...

Every finite group of order n can be represented as a permutation group on n letters, as first proved by Cayley in 1878 (Rotman 1995).

Let p be a prime number, G a finite group, and |G| the order of G. 1. If p divides |G|, then G has a Sylow p-subgroup. 2. In a finite group, all the Sylow p-subgroups are ...

Every finite simple group (that is not cyclic) has even group order, and the group order of every finite simple noncommutative group is doubly even, i.e., divisible by 4 ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...