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Some Related Sentences
Every and group
Every finite simple
group is isomorphic to one of
the following
groups:

Group actions / representations:
Every group G
can be considered as
a category
with a single object whose morphisms
are the elements of G
. A functor from G to Set is then nothing but
a group action of G on
a particular set, i
. e
. a G-set
.

*
Every group G acts on G, i
. e
. in two natural but essentially different ways:, or
.
Every galaxy of sufficient mass in
the Local Group has an associated
group of globular clusters, and almost every large galaxy surveyed has been found to possess
a system of globular clusters
.

*
Every Lie
group is parallelizable, and hence an orientable manifold ( there is
a bundle isomorphism between its tangent bundle and
the product of itself
with the tangent space at
the identity )
Every instrumental
group ( or section ) has
a principal who is generally responsible for leading
the group and playing orchestral solos
.

*
Every closed subgroup of
a profinite
group is itself profinite
; the topology arising from
the profiniteness agrees
with the subspace
topology.

While he admits
the existence of caste-based discrimination, he writes that "
Every social
group cannot
be regarded as
a race simply because we want to protect
it against prejudice and discrimination ".
Every local
group is required to have
a seneschal who reports to
the kingdom's seneschal
.
Every local
group is required to have one
.

*
Every topological group is completely regular
.
Every summer
the group gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying
the splendors of
the Gilded Age
.

*
Every finitely generated
group with a recursively enumerable presentation and insoluble word problem is
a subgroup of
a finitely presented
group with insoluble word problem
Every synset contains
a group of synonymous words or collocations (
a collocation is
a sequence of words that go together to form
a specific meaning,
such as " car pool "); different senses of
a word
are in different synsets
.
Every topological group can be viewed as
a uniform space in two ways
; the left uniformity turns all left multiplications
into uniformly continuous maps while
the right uniformity turns all right multiplications
into uniformly continuous maps
.
Every subgroup of
a topological group is itself
a topological group when given
the subspace
topology.

:"
Every group is naturally isomorphic to its opposite
group "
Every ten years, when
the general census of population takes place, each citizen has to declare which linguistic
group they belong or want to
be aggregated to
.
Every and can
Every such subset has
a smallest element, so to specify our choice function we
can simply say that
it maps each set to
the least element of that set
.

** Well-ordering theorem:
Every set
can be well-ordered
.
Every information exchange between living organisms — i
. e
. transmission of signals that involve
a living sender and receiver
can be considered
a form of communication
; and even primitive creatures
such as corals
are competent to communicate
.
Every context-sensitive grammar which does not generate
the empty string
can be transformed
into an equivalent one in Kuroda normal form
.

*
Every regular language is context-free because
it can be described
by a context-free grammar
.
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar
can be transformed
into an equivalent one which is in Chomsky normal form
.
Every real number has
a ( possibly infinite ) decimal representation
; i
. e.,
it can be written as
Every module over
a division ring has
a basis
; linear maps between finite-dimensional modules over
a division ring
can be described
by matrices, and
the Gaussian elimination algorithm remains applicable
.
Every entire function
can be represented as
a power series that converges uniformly on compact sets
.
Every positive integer n > 1
can be represented in exactly one way as
a product of prime powers:
Every sequence
can, thus,
be read in three reading frames, each of which will produce
a different amino acid sequence ( in
the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).
Every hyperbola is congruent to
the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to
the origin-centered North-South opening hyperbola
with identical eccentricity ε — that is,
it can be rotated so that
it opens in
the desired direction and
can be translated ( rigidly moved in
the plane ) so that
it is centered at
the origin
.
Every holomorphic function
can be separated
into its real and imaginary parts, and each of these is
a solution of Laplace's equation on R < sup > 2 </ sup >.
Every species
can be given
a unique ( and, one hopes, stable ) name, as compared
with common names that
are often neither unique nor consistent from place to place and language to language
.
Every vector v in determines
a linear map from R to taking 1 to v, which
can be thought of as
a Lie algebra homomorphism
.
Every morpheme
can be classified as either free or bound
.
Every use of modus tollens
can be converted to
a use of modus ponens and one use of transposition to
the premise which is
a material implication
.
Every document window is an object
with which
the user
can work
.
Every adult, healthy, sane Muslim who has
the financial and physical capacity to travel to Mecca and
can make arrangements for
the care of his / her dependants during
the trip, must perform
the Hajj once in
a lifetime
.
Every ordered field
can be embedded
into the surreal numbers
.

*
Every finite
topological space gives rise to
a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder
can be formed as
the specialization preorder of
a topological space in this way
.

*
Every preorder
can be given
a topology,
the Alexandrov
topology ; and indeed, every preorder on
a set is in one-to-one correspondence
with an Alexandrov
topology on that set
.
Every binary relation R on
a set S
can be extended to
a preorder on S
by taking
the transitive closure and reflexive closure, R < sup >+=</ sup >.
0.084 seconds.