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Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then a literal obtained from ...

The set of points of X fixed by a group action are called the group's set of fixed points, defined by {x:gx=x for all g in G}. In some cases, there may not be a group action, ...

The kernel of a group homomorphism f:G-->G^' is the set of all elements of G which are mapped to the identity element of G^'. The kernel is a normal subgroup of G, and always ...

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

If G is a group, then the torsion elements Tor(G) of G (also called the torsion of G) are defined to be the set of elements g in G such that g^n=e for some natural number n, ...

If G is a perfect group, then the group center of the quotient group G/Z(G), where Z(G) is the group center of G, is the trivial group.

A necessary and sufficient condition that there should exist at least one nondecreasing function alpha(t) such that mu_n=int_(-infty)^inftyt^ndalpha(t) for n=0, 1, 2, ..., ...

A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {U_alpha} such that every real number beta has a unique ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...