Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.

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 normal regular space is completely regular, and every normal Hausdorff space is Tychonoff.

Every time the Flaminica saw a lightning bolt ( Jupiter's distinctive instrument ), she was prohibited from carrying on with her normal routine until she placated the gods.

* Every connected graph with only countably many vertices admits a normal spanning tree.

Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form.

Every Hermitian matrix is a normal matrix, and the finite-dimensional spectral theorem applies.

Every generalized eigenvalue of a normal operator is thus genuine.

Every formula in classical logic is equivalent to a formula in prenex normal form.

Every first-order formula is logically equivalent ( in classical logic ) to some formula in prenex normal form.

Every first-order formula can be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization ( sometimes spelled " Skolemnization ").

:* Every generalized eigenvector of a normal matrix is an ordinary eigenvector.

Every zombie is restored to normal when Hal Jordan defeats Nekron.

Every year the club hosts a two week long ( three weekends ) camp at Bohemian Grove, which is notable for its illustrious guest list and its eclectic Cremation of Care ceremony which mockingly burns " Care " ( the normal woes of life ) with grand pageantry, pyrotechnics and brilliant costumes, all done at the edge of a lake and at the base of a forty-foot ' stone ' owl statue.

One particular ad line read " Every normal skin needs these two creams ".

Every normal mammalian eye has a scotoma in its field of vision, usually termed its blind spot.

Every ( normal ) Boolean algebra with operators can be represented as a field of sets on a relational structure in the sense that it is isomorphic to the complex algebra corresponding to the field.

Every grammar in Kuroda normal form is monotonic, and therefore, generates a context-sensitive language.

Every year thereafter Battle Bowl took place with only one ring and a normal battle royal.

Every homeworld ( except Gnasty's World ) contains a flying challenge level where Spyro's normal gliding ability is replaced with the ability to fly freely.

Every self-adjoint operator is normal.

Every ( nontrivial ) group has a normal series of length 1, namely

Every beach soccer match is won by one team, with the game going into three minutes of extra time, followed by a penalty shootout if the score is still on level terms after normal time.

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

* 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 subgroup of a topological group is itself a topological group when given the subspace topology.

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

Every subgroup of a free abelian group is itself free abelian, which is important for the description of a general abelian group as a cokernel of a homomorphism between free abelian groups.

Every group of prime order is cyclic, since Lagrange's theorem implies that the cyclic subgroup generated by

Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.

* Every subgroup and quotient group of a locally cyclic group is locally cyclic.

* Every triangle group T is a discrete subgroup of the isometry group of the sphere ( when T is finite ), the Euclidean plane ( when T has a Z + Z subgroup of finite index ), or the hyperbolic plane.

Every compact Lie group G of dimension > 0 has a subgroup isomorphic to the circle group.

* Every ( closed ) subgroup of an amenable goup is amenable.

Recall that a subsemigroup G of a semigroup S is a subgroup of S ( also called sometimes a group in S ) if there exists an idempotent e such that G is a group with identity element e. A semigroup S is group-bound if some power of each element of S lies in some subgroup of S. Every finite semigroup is group-bound, but a group-bound semigroup might be infinite.

Every subgroup is organized around a set of brothers, each of whom is often married to a group of sisters.

Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.

Every proper subgroup of G can be assumed a solvable group, meaning that much theory of such subgroups could be applied.

Every closed subgroup of a locally compact group is locally compact.

Every quasinormal subgroup is a modular subgroup, that is, a modular element in the lattice of subgroups.

Every quasinormal subgroup is conjugate permutable.

Every group has itself ( the improper subgroup ) and the trivial subgroup as two of its fully characteristic subgroups.