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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 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 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 ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

The set of all ground atoms that can be formed from predicate symbols from a clause in Skolemized form S and terms from the Herbrand universe H of S.

Let A be a C^*-algebra. A C^*-subalgebra (that is a closed *-subalgebra) B of A is called hereditary if bab^' in B for all b,b^' in B and a in A, or equivalently if for a in ...

The Heronian mean of two numbers a and b is defined as HM(a,b) = 1/3(2A+G) (1) = 1/3(a+sqrt(ab)+b), (2) where A is the arithmetic mean and G the geometric mean. It arises in ...