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Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...

The group of functions from an object G to itself which preserve the structure of the object, denoted Aut(G). The automorphism group of a group preserves the multiplication ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...

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| = ...

When working over a collection of fields, the base field is the intersection of the fields in the collection, i.e., the field contained in all other fields.

For P, Q, R, and S polynomials in n variables [P·Q,R·S]=sum_(i_1,...,i_n>=0)A/(i_1!...i_n!), (1) where A=[R^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n) ...

If g(theta) is a trigonometric polynomial of degree m satisfying the condition |g(theta)|<=1 where theta is arbitrary and real, then g^'(theta)<=m.

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

Let the nth composition of a function f(x) be denoted f^((n))(x), such that f^((0))(x)=x and f^((1))(x)=f(x). Denote the composition of f and g by f degreesg(x)=f(g(x)), and ...