* Let H be a group, and let G be the direct product H × H. Then the subgroups

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).

Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).

Let f and g be any two elements of G. By virtue of the definition of G, = and =, so that =.

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Let a, b, and c be elements of G. Then:

Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD.

Let R be a ring and G be a monoid.

Let this point be called G. Point G is also the midpoint of line segment FQ:

Let F and G be a pair of adjoint functors with unit η and co-unit ε ( see the article on adjoint functors for the definitions ).

Let G and H be groups, and let φ: G → H be a homomorphism.

Let G be a group.

Let S be a subgroup of G, and let N be a normal subgroup of G. Then:

Let G be a group.

Let N and K be normal subgroups of G, with

Let X be a topological space which is the union of two open and path connected subspaces ,.

The lead track " Don't Let Him Know ", written by Jim Vallance and Bryan Adams, became Prism's first top 40 hit in the US and a # 1 single on Billboard's new Rock Tracks chart ,.

For example, proverbs have been used for teaching foreign languages at various levels., In addition, proverbs have been used for public health promotion, such as promoting breast feeding with a shawl bearing a Swahili proverb “ Mother ’ s milk is sweet ”, also for helping people manage diabetes, for to combat prostitution, and for community development The most active field deliberately using proverbs is Christian ministry, where Joseph G. Healey and others have deliberately worked to catalyze the collection of proverbs from smaller languages and the application of them in a wide variety of church-related ministries, resulting in publications of collections and applications ,.

Aktien-Gesellschaft „ Weser ”-short A. G. „ Weser ”-was founded as a successor of the 1843 founded Eisengiesserei & Maschinenbau-Anstalt Waltjen und Leonhard ,.

* R. Behringer, G. Klinker ,.

After the finishing process, the genome sequence was found to contain 3, 268, 203 base pairs ( bp ), and to have an average G + C content of 57. 8 %, values much lower than the corresponding values for M. tuberculosis, which are 4, 441, 529 bp and 65. 6 % G + C ,.

The following year S. G. Warburg was purchased by Swiss Bank Corporation ,.

Crosby and Root's first successful popular songs was " The Hazel Dell " ( 1853 ), a " sentimental ballad " described by its publisher as " a very pretty and easy song, containing the elements of great popularity ", which was released as the work of G. F. Wurzel toward the end of 1853, and was a hit, that was " one of the most popular songs in the country ", because of its performance by both Henry Wood's Minstrels and Christy's Minstrels, selling more than 200, 000 copies of sheet music ,.

Cook, G ,.