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* 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

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## Some Related Sentences

Every and finitely

Hilbert's example: " the assertion that either there are only

__finitely__many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 );**and**Brouwer's: "__Every__mathematical species**is**either finite or infinite.
#

__Every____finitely__**generated**ideal**of**A**is**principal ( i. e., A**is****a**Bézout domain )**and**A satisfies the ascending chain condition on principal ideals.__Every__subset

**of**

**a**nowhere dense set

**is**nowhere dense,

**and**the union

**of**

__finitely__many nowhere dense sets

**is**nowhere dense.

*****

__Every__left ideal I in R

**is**

__finitely__

**generated**, i. e. there exist elements

**a**< sub > 1 </ sub >, ...,

**a**< sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.

__Every__

__finitely__

**presented**

**group**

**is**

**recursively**

**presented**, but there are

**recursively**

**presented**groups that cannot be

__finitely__

**presented**.

__Every__one

**of**the infinitely many vertices

**of**G can be reached from v < sub > 1 </ sub >

**with**

**a**simple path,

**and**each such path must start

**with**one

**of**the

__finitely__many vertices adjacent to v < sub > 1 </ sub >.

" I can now state the physical version

**of**the Church-Turing principle: '__Every____finitely__realizable physical system can be perfectly simulated by**a**universal model computing machine operating by finite means.*****

__Every__substructure

**is**the union

**of**its

__finitely__

**generated**substructures ; hence Sub ( A )

**is**an algebraic lattice.

A finitely-generated abelian

**group****is**indecomposable if**and**only if it**is**isomorphic to Z or to**a**factor**group****of**the form for some prime number p**and**some positive integer n.__Every__finitely-generated abelian**group****is****a**direct sum**of**(__finitely__many ) indecomposable abelian groups.
This

**is**up to isomorphism the only indecomposable module over R.__Every__left R-module**is****a**direct sum**of**(__finitely__or infinitely many ) copies**of**this module K < sup > n </ sup >.__Every__( bounded ) convex polytope

**is**the image

**of**

**a**simplex, as every point

**is**

**a**convex combination

**of**the (

__finitely__many ) vertices.

Every and generated

__Every__

**group**

**of**prime order

**is**cyclic, since Lagrange's theorem implies that the cyclic

**subgroup**

__generated__by

__Every__lattice in can be

__generated__from

**a**basis for the vector space by forming all linear combinations

**with**integer coefficients.

__Every__film today, whether it be live-action, computer

__generated__, or traditional hand-drawn animation

**is**made up

**of**hundreds

**of**individual shots that are all placed together during editing to form the single film that

**is**viewed by the audience.

A large part

**of**the interest__generated__was due to the eclectic mix**of**samples**and**influences, evident on__Every__Man**and**Woman, which was dedicated to Dewey Bunnell**of**the band America.__Every__ticket

__generated__by the system has persistence or " history " showing what happened to the ticket within its life cycle.

__Every__profile also captures some non-crime statistics: the amount

**of**overtime

__generated__by members

**of**the command, the number

**of**department vehicle accidents, absence rates due to sick time

**and**line-of-duty injuries,

**and**the number

**of**civilian complaints lodged against members

**of**the unit.

Every and group

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__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__summer the

__group__gathers in Newport, RI for week long dance training, seaside teas,

**and**evenings enjoying the splendors

**of**the Gilded Age.

__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__

__group__can be trivially made into

**a**topological

__group__by considering it

**with**the discrete topology ; such groups are called discrete groups.

__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__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.

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