The three classes are groups of GF ( 2 ) type ( classified mainly by Timmesfeld ), groups of " standard type " for some odd prime ( classified by the Gilman – Griess theorem and work by several others ), and groups of uniqueness type, where a result of Aschbacher implies that there are no simple groups.

which can be seen to hold for all integers k, together with Euler's formula, implies several trigonometric identities as well as de Moivre's formula.

This fact has several important consequences in science: first, it prohibits " perpetual motion " machines ; and second, it implies the arrow of entropy has the same direction as the arrow of time.

Heinlein challenges his readers ' possible racial preconceptions by introducing a strong, sympathetic character, only to reveal much later that he or she is of African or other descent ; in several cases, the covers of the books show characters as being light-skinned, when in fact the text states, or at least implies, that they are dark-skinned or of African descent.

The fact that some parts of the codex are preserved in good condition, while others are in very poor condition, implies they were separated and stored in several places.

Eland are very frequently depicted in the rock art of the region, which implies that they were viewed as having a strong connection to the other world, and in several languages the word for eland and for dance is the same ; significant because shamans used dance as their means of drawing power from the other world.

Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).

As the title implies, several rap musicians have appeared on the panel, along with an assortment of stand-up comics, NYC radio personalities, and stars from other MTV and MTV2 series.

A 10-minute standing ovation followed the concert ; the DVD shows several rock luminaries in the crowd, such as Roger Daltrey, Paul Weller, Sir George Martin and Sir Paul McCartney ( although neither Martin nor McCartney attended the opening night, contrary to what the DVD implies ).

The evil Supergirl implies that Kara's family sent her to Earth to kill Kal-El as revenge for a family grudge ; at the time, Kara herself refuses to believe this, but later flashbacks indicate that not only is this partly true, but Kara had been physically altered by her father as a child before being involved in several murders on Krypton.

As its name implies, Lakeville contains several lakes as well as smaller ponds and wetlands within its borders.

Unlike other methods of ergonomics, focus group implies several participants: users or future users of the application.

Decennial implies that this occurs every ten years, but in the past several decades, there have been Decennial Digest Parts I and II ( the 11th Series now has Part III ), so the cumulation is now more frequent.

It was proposed by, and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture.

" This implies that the Terrans still know about Earth but its location is lost ( StarCraft manual mentions that the sleeper ships have became lost in hyperspace when an error erased the intended destination's coordinates, as well as those of Earth's, resulting in the ships going at full speed for several decades until the engines broke down ).

As their name implies, treecreepers forage for insects and other small creatures living on and under the bark of trees, mostly eucalypts, though several species also hunt on the ground, through leaf-litter, and on fallen timber.

" Dialogue between several characters implies that young Clark is a costumed adventurer, but he is never referred to as " Superboy ".

There are several extra conditions which ensure that the vanishing of the Wronskian in an interval implies linear dependence.

The more complex Multi-Step income statement ( as the name implies ) takes several steps to find the bottom line, starting with the gross profit.

In modern console games, arcade games, and personal computer games, multiplayer usually implies that the players play together by using several controllers plugged into the same game system.

This, however, implies a reliance on a dominant-party system, and several opposition critics find this as evidence for contempt for the political opposition in Singapore.

As the name implies, it features several speech clips, including " intruder alert " and " I'll get you next time ".

As the name implies, the " tube " of this design is actually composed of an upper ' cage assembly ', which contains the secondary mirror, and focuser, held in place by several rigid poles over a ‘ mirror box ’ which contains the objective mirror.

Because WMI abstracts the manageable entities with CIM and a collection of providers, the development of a provider implies several steps.

In contrast to this Stoic-patristic view, Utopia implies that the nature of man is such that to rely on individual conscience to supply the deficiencies of municipal law is to embark on the bottomless sea of human sinfulness in a sieve.

A sequence is an absolute measure of base composition of an individual, or a representative of a species or group ; a genotype typically implies a measurement of how an individual differs or is specialized within a group of individuals or a species.

This implies that if and are independent, then their joint entropy is the sum of their individual entropies.

An EU case concerning Italy extended this principle to the rest of the EU in that it stated that, " The principle of trade union freedom in the Italian system implies recognition of the right of the individual not to belong to any trade union (" negative " freedom of association / trade union freedom ), and the unlawfulness of discrimination liable to cause harm to non-unionized employees.

The term " media bias " implies a pervasive or widespread bias contravening the standards of journalism, rather than the perspective of an individual journalist or article.

In shifting the debate from " what is true " to " of what can I be certain ?," Descartes shifted the authoritative guarantor of truth from God to Man ( While traditional concept of " truth " implies an external authority, " certainty " instead relies on the judgement of the individual Man ).

In QCD this phenomenon is called color confinement ; it implies that only hadrons, not individual free quarks, can be observed.

Robert Jenson suggests that Gregory implies that each member of the Godhead has an individual priority: the Son has epistemological priority, the Father has ontic priority and the Spirit has metaphysical priority.

The term bi-curious implies that the individual has either no or limited homosexual experience in the case of " heterosexual " individuals or no or limited heterosexual experience in the case of " homosexuals ", but may continue to self-identify as bi-curious if they do not feel they have adequately explored these feelings, or if they do not wish to identify as bisexual.

The term " media bias " implies a pervasive or widespread bias contravening the standards of journalism, rather than the perspective of an individual journalist or article.

Neoclassical economics by contrast refers to " the individual in whom the human capital is ... embedded ", which implies a strong association of the individual with the instructional capital they learn from, with little or no social capital influence.

For example, in the religious realm, free will implies that individual will and choices can coexist with an omnipotent divinity.

Solo billing usually implies that the individual is more prominent in the musical arrangement.

This end usually implies a moral upliftment or progress of an individual or society.

* creativity ( individual capital ) which implies rights to benefit from one's free expression

* Example: The " Support Our Troops " campaign created by the Republican party during the War on Terror implies that opposing the war effort detracts support away from the individual soldiers fighting the war.

This implies that the inventions, which involve a delicate change in the manufacturing process, were being passed from one individual to another.

An individual demonstrating this false compromise fallacy implies that the positions being considered represent extremes of a continuum of opinions, and that such extremes are always wrong, and the middle ground is always correct.

The school resumed its individual status in 1949 and went on to be known as St. Paul's College once again when its campus on Bonham Road was completed, while St. Paul's Co-educational College remained, as its name implies, co-educational.

However, the extent to which individual instances of deaths resulted in veneration ( glorification ) implies that was not very common.

Edges between nodes represent individual molecular reactions, the protein / protein and protein / mRNA interactions through which the products of one gene affect those of another, though the lack of experimentally obtained information often implies that some reactions are not modeled at such a fine level of detail.

It suffices to take for d the degree of the symmetric function, since the part in degree d is of that ring is mapped isomorphically to rings with more indeterminates by φ < sub > n </ sub > for all n ≥ d. This implies that for studying relations between individual elements, there is no fundamental difference between symmetric polynomials and symmetric functions.