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Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.

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## Some Related Sentences

Any and formal

__Any__

__formal__or informal

**group**— a family

**,**a church

**,**a club

**,**a business

**,**a trade union — may be said to have government

**.**

__Any__

__formal__series with has a composition inverse provided is

**an**invertible element

**of**

**R**

**.**The coefficients are found recursively from

**the**above formula for

**the**coefficients

**of**a composition

**,**equating them with those

**of**

**the**composition identity X ( that is 1 at degree 1 and 0 at every degree greater than 1 )

**.**

__Any__

__formal__policy guidelines issued by

**the**chancellor are legally binding directives that cabinet ministers must implement

**.**

__Any__nation

**,**with or without

__formal__relations

**,**may request

**the**extradition

**of**fugitives who abscond to Bhutan

**.**

__Any__proposal

**of**

**law**

**in**

**the**broadest sense and any proposed treaty is

**in**principle first submitted to

**the**Council

**of**State for legal comment ; this can be limited by

__formal__

**law**

**,**which however only does so for trivial cases ( Article 73 ).

#

__Any__assignment**of****the**elements**of**a__formal__language to natural numbers**in**such a way that**the**numbers can be manipulated by**an**algorithm to simulate manipulation**of**elements**of****the**__formal__language**.**
It also includes force used directly to preclude or impede

**the**mission and / or duties**of**US forces**,**including**the**recovery**of**US personnel or vital US Government property .” A “ hostile force ” is**defined**as “__Any__civilian**,**paramilitary**,**or military force or terrorist ( s ), with or without national designation**,**that have committed a hostile act**,**exhibited hostile intent**,**or have been declared hostile by appropriate US authority .” “ Armed forces ” are**defined**as “ The military forces**of**a nation or a**group****of**nations .” Although**the**original Senate bill that produced**the**1989 amendment intended to make**the**treatment**of**captives**the**operative qualifying condition for those held outside**of**__formal__armed conflict**,**this intent has only been sporadically enforced**.**__Any__person or organization

**,**public or private

**,**may make inquiries or request

**the**Board to render

__formal__decisions on proposed new names

**,**proposed name changes

**,**or names that are

**in**conflict

**.**

Allen's

__formal__definition is found on page 4**of****the**original edition**of****the**book: "__Any__voting system**in**which**the**mechanisms for recording and / or tabulating**the**vote are hidden from**the**voter**,**and / or**the**mechanism lacks a tangible record**of****the**vote cast**.**__Any__dentist

**in**

**the**UK who wishes to train

**in**

**the**field

**of**dental implantology must take

**part**

**in**

**an**extended learning program which covers a detailed theory syllabus

**,**as approved by

**the**GDC

**,**

**in**addition to

__formal__supervised surgical training and mentoring

**.**

* Cheating:

__Any__attempt to give or obtain assistance**in**a__formal__academic exercise ( like**an**examination ) without due acknowledgment**.**__Any__Chinese citizen with

**the**right to vote who has passed a professional competency test after

__formal__training or after two to three years

**of**experience

**in**legal work could qualify as a lawyer

**.**

Any and group

__Any__normal subgroup has a corresponding quotient

__group__

**,**formed from

**the**larger

__group__by eliminating

**the**distinction between elements

**of**

**the**subgroup

**.**

*

__Any__simply connected solvable**Lie**__group__is isomorphic to a closed subgroup**of****the**__group__**of**invertible upper triangular matrices**of**some rank**,**and any finite**dimensional**irreducible representation**of**such a__group__is 1**dimensional****.**
*

__Any__simply connected nilpotent**Lie**__group__is isomorphic to a closed subgroup**of****the**__group__**of**invertible upper triangular matrices with 1's on**the**diagonal**of**some rank**,**and any finite**dimensional**irreducible representation**of**such a__group__is 1**dimensional****.**__Any__

**Lie**

__group__G can be decomposed into discrete

**,**simple

**,**and abelian groups

**in**a canonical way as follows

**.**

#

__Any__tangent vector at**the**identity**of**a**Lie**__group__can be extended to a left invariant vector field by left translating**the**tangent vector to other points**of****the**manifold**.**
"

__Any__attempt to organize**the**__group__... under a single authority would eliminate their independent initiatives**,**and thus reduce their joint effectiveness to that**of****the**single person directing them from**the**centre**.**__Any__symmetry

__group__whose elements have a common fixed point

**,**which is true for all finite symmetry groups and also for

**the**symmetry groups

**of**bounded figures

**,**can be represented as a subgroup

**of**orthogonal

__group__O (

**n**) by choosing

**the**origin to be a fixed point

**.**

However

**,****in****the**case**of**a finitely presented__group__we know that not all**the**generators can be trivial (__Any__individual generator could be**,****of**course ).__Any__

__group__that managed to find ways

**of**reasoning effectively would reap benefits for all its members

**,**increasing their fitness

**.**

__Any__time during a triad conversation

**,**

__group__members can switch seats and one

**of**

**the**co-pilots can sit

**in**

**the**pilot ’ s seat

**.**

__Any__

__group__can be seen as a category with a single object

**in**which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing

**the**

__group__as acting on itself by left multiplication

**.**

Any and law

__Any__person who felt himself wronged might lay

**an**information before

**the**Council

**of**Areopagus

**,**on declaring what

__law__was broken by

**the**wrong done to him

**.**

__Any__person could develop and use a coat

**of**arms if they wished to do so

**,**provided they did not usurp someone else's arms

**,**and historically

**,**this right was enshrined

**in**Roman Dutch

__law__

**.**

In

**an**inertial frame**,**Newton's first__law__(**the**__law__**of**inertia ) is satisfied:__Any__free motion has a constant magnitude and direction**.**
The

__law__states that “__Any__person who is arrested shall have**the**person ’ s immigration status determined before**the**person is released ”.__Any__conductor

**,**be it a loop

**,**a coil or simply a piece

**of**plate metal

**,**that is placed

**in**this field will have eddy currents induced

**in**it thus creating

**an**opposing magnetic field

**,**

**in**accordance with Lenz's

__law__

**.**

* Noether's theorem:

__Any__quantity which has a continuous differentiable symmetry**in****the**action has**an**associated conservation__law__**.**
Today lynching is a felony

**in**all states**of****the**United States**,****defined**by some codes**of**__law__as "__Any__act**of**violence inflicted by a mob upon**the**body**of**another person which results**in****the**death**of****the**person ," with a " mob " being**defined**as "**the**assemblage**of**two or more persons**,**without color or authority**of**__law__**,**for**the**premeditated purpose and with**the**premeditated intent**of**committing**an**act**of**violence upon**the**person**of**another**.**
:( c )

__Any__public safety officer**,**sheriff's deputy or officer authorized by__law__may seize or arrange for**the**removal**of**any Pit Bull Terrier from**the**city**.**__Any__means

**,**

**in**short

**,**whereby

**the**general

__law__

**of**tithing is altered

**,**and a new method

**of**taking them is introduced

**,**is called a modus decimandi

**,**or special manner

**of**tithing

**.**

*

__Any__use whatsoever**of**matrimony exercised**in**such a way that**the**act is deliberately frustrated**in**its natural power to generate life is**an**offense against**the**__law__**of**God and**of**nature**,**and those who indulge**in**such are branded with**the**guilt**of**a grave sin**.**__Any__

__law__passed by

**the**District legislature can be nullified by Congressional action

**,**and indeed

**the**District government could be significantly altered or eliminated entirely by a simple majority vote

**in**Congress

**.**

(

**2**)__Any__non-profit corporation**,**civic association**,**or governmental entity which has buildings and grounds open to**the**public may request for**the**appointment**of**constables to serve as__law__enforcement officers**in**order to protect life and property**.**__Any__similar canister with

**the**labels reading " dog spray " and / or " bear spray " is regulated under

**the**Pest Control Products Act-while legal to be carried by anyone

**,**it is against

**the**

__law__if its use causes ' a risk

**of**imminent death or serious bodily harm to another person ' or harming

**the**environment and carries a penalty up to a fine

**of**$ 500

**,**000 and jail time

**of**maximum 3 years

**.**

__Any__person accused

**of**committing a crime is presumed innocent until proven guilty

**in**a court

**of**

__law__

**.**

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