Every quasinormal subgroup is conjugate permutable.

Every normal subgroup is quasinormal, because, in fact, a normal subgroup commutes

* Every quasinormal subgroup, and, more generally, every conjugate permutable subgroup, of a finite group is subnormal.

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

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every bounded positive-definite measure μ on G satisfies μ ( 1 ) ≥ 0. improved this criterion by showing that it is sufficient to ask that, for every continuous positive-definite compactly supported function f on G, the function Δ < sup >– ½ </ sup > f has non-negative integral with respect to Haar measure, where Δ denotes the modular function.

Every distributive lattice is modular.

Every AP defines a top data models to be used for data exchange, called the Application Integrated Model ( AIM ) or in the case of a modular AP called Module Integrated Models ( MIM ).

Every modular function will have this general kind of self-similarity.

Every modular function will have this general kind of self-similarity.