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Page "Classification of finite simple groups" ¶ 35
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If and group
`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.
If coffee is sold at the cafeteria, let a few workers in each department get it for the whole group.
If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.
If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.
If the joining of monomers takes place at such a carbon atom, the free hydroxy group of the pyranose or furanose form is exchanged with an OH-side-chain of another sugar, yielding a full acetal.
If the amino group is removed from an amino acid, it leaves behind a carbon skeleton called an α-keto acid.
If a bubble touches identically-colored bubbles, forming a group of three or more, those bubbles — as well as any bubbles hanging from them — are removed from the field of play, and points are awarded.
If the Bastarnae remained an identifiable group, it is highly likely that they participated in the vast Gothic-led migration, driven by Hunnic pressure, that was admitted into Moesia by emperor Valens in 376 and eventually defeated and killed Valens at Adrianople in 378.
* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).
If the carbonyl group is an aldehyde, the monosaccharide is an aldose ; if the carbonyl group is a ketone, the monosaccharide is a ketose.
If there is a tie, we must consider the atoms at distance 2 from the stereocenter — as a list is made for each group of the atoms bonded to the one directly attached to the stereocenter.
If the addition of a functional group takes place at the less substituted carbon atom of the double bond, then the electrophilic substitution with acids is not possible.
If n ≥ 1 and is an integer, the numbers coprime to n, taken modulo n, form a group with multiplication as operation ; it is written as ( Z / nZ )< sup >×</ sup > or Z < sub > n </ sub >< sup >*</ sup >.
If G is a group, and g is a fixed element of G, then the conjugation map
If a database cannot tolerate even such smaller probability of data loss, then the RAID group itself is replicated ( mirrored ).
If a database cannot tolerate even such smaller probability of data loss, then the RAID group itself is replicated ( mirrored ).
* If we think of as the group of real numbers under addition, then the direct product still consists of.
If the ether is part of a more complex molecule, it is described as an alkoxy substituent, so-OCH < sub > 3 </ sub > would be considered a " methoxy -" group.
If there is another functional group at a carbon, it may be named with the Greek letter, e. g., the gamma-amine in gamma-aminobutanoic acid is on the third carbon of the carbon chain attached to the carboxylic acid group.
Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.

If and has
`` If Blue Throat has his way he'll keep us all cooped up in here for days '', he said.
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.
If this new Bible does not increase in significance by repeated readings throughout the years, it will not survive the ages as has the King James Version.
If the case is thus determined by us to be domestic, the court has no jurisdiction.
If this capacity had not failed them, they would see that their enemy has made a disastrous miscalculation.
If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.
If the superintendents do not receive more cooperation from Handlers, it has been suggested that licensed Judges also be qualified to judge this Class.
If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.
If design head has a deep cavity, clay lid will be quite thick at this point ; ;
If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.
If we manage to keep track of a Bombus queen after she has left her feeding place, we may discover the snug little hideout which she has fixed up for herself when she woke up from her winter sleep.
If cell Af has not previously been assigned as the information cell of a form in the text-form list, it is now assigned as the information cell of Af.
If of the founders of glottochronology Swadesh has escaped our steady plodding, and Lees has repudiated his own share in the founding, that is no reason why we should swerve.
If the transferor has substantial assets other than the claim, it seems reasonable to assume no corporation would be willing to acquire all of its properties in the dim hope of collecting a claim for refund of taxes.
If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.
If the distant patron of the suburban branch has been frightened away from downtown by traffic problems, however, the city store can only pressure the politicians to do something about the highways or await the completion of the federal highway program.
If a statement has been assigned an address in the index word area
If she has not had such experiences, the female's normal adolescent degree of indecision will be compounded.
If Barnett doesn't call a special session in 1961, it will be the first year in the last decade that the Legislature has not met in regular or special session.
If the church has followed the plan of cultivation of prospects and carried through a program of membership preparation as outlined earlier in this book, the process of assimilation and growth will be well under way.

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