The simple pragmatic success of the sociology of small groups needs to be questioned.

The solution of the problem is a special case of a Steiner system, which systems play an important role in the classification of finite simple groups.

In this technique, the total population is divided into these groups ( or clusters ) and a simple random sample of the groups is selected.

The number of Conservative groups, their lack of stability, and their tendency to be identified with local issues defy simple categorization.

The Crucifix, a cross with the corpus ( Body of Christ ), is an ancient symbol used within the Catholic, Eastern Orthodox, Anglican, and Lutheran churches, in contrast with some Protestant groups, which use only a simple cross.

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below.

Every finite simple group is isomorphic to one of the following groups:

** the classical Lie groups, namely the simple groups related to the projective special linear, unitary, symplectic, or orthogonal transformations over a finite field ;

* The 26 sporadic simple groups.

The classification theorem has applications in many branches of mathematics, as questions about the structure of finite groups ( and their action on other mathematical objects ) can sometimes be reduced to questions about finite simple groups.

Thanks to the classification theorem, such questions can sometimes be answered by checking each family of simple groups and each sporadic group.

Daniel Gorenstein announced in 1983 that the finite simple groups had all been classified, but this was premature as he had been misinformed about the proof of the classification of quasithin groups.

The simple groups of small 2-rank include:

The Sylow 2-subgroups are either cyclic, which is easy to handle using the transfer map, or generalized quaternion, which are handled with the Brauer – Suzuki theorem: in particular there are no simple groups of 2-rank 1.

The first case was done by the Gorenstein – Walter theorem which showed that the only simple groups are isomorphic to L < sub > 2 </ sub >( q ) for q odd or A < sub > 7 </ sub >, the second and third cases were done by the Alperin – Brauer – Gorenstein theorem which implies that the only simple groups are isomorphic to L < sub > 3 </ sub >( q ) or U < sub > 3 </ sub >( q ) for q odd or M < sub > 11 </ sub >, and the last case was done by Lyons who showed that U < sub > 3 </ sub >( 4 ) is the only simple possibility.

As she was rather tired this evening, her simple `` Thank you for the use of your bath '' -- when she sat down opposite him -- spoken in a low voice, came across with coolnesses of intelligence and control.

The answer is simple: most species have a negligible vapour pressure at such low temperatures and this means that they quickly condense on the sides of the apparatus.

Often, simple dives with low DDs will look good to spectators but will not win meets.

Fruit flies are often preferred over other animals due to their short life cycle, low maintenance requirements, and relatively simple genome compared to many vertebrates.

PIP with a very low baud rate ( because it had no built-in error correction ) could be used to transfer a small simple version of Kermit from one machine to another over a null modem cable, or failing that, a very very simple version of the Kermit protocol could be hand coded in binary in less than 2K using DDT, the CP / M Dynamic Debugging Tool.

Because of this sensitivity to infant mortality, simple life expectancy at age zero can be subject to gross misinterpretation, leading one to believe that a population with a low overall life expectancy will necessarily have a small proportion of older people.

If the true function is simple, then an " inflexible " learning algorithm with high bias and low variance will be able to learn it from a small amount of data.

Because of their low-rise construction ( most were simple one-story buildings, anything more than two floors with outside corridors being rare ) with large car parks, the number of rooms which would fit on any given amount of land was low compared to the high-rise urban hotels which had grown around railway stations.

If they both used the Attic stadion of about 185 meters, then the older estimate is 1 / 6 too large, and Ptolemy's value is 1 / 6 too small, a difference explained as due to ancient scientists ' use of simple methods of measuring the earth, which were corrupted either high or low by a factor of 5 / 6, due to air's bending of horizontal light rays by 1 / 6 of the Earth's curvature.

This algorithm has the advantage of being simple while having a low requirement for computing resources.

The simple fixed-size-blocks algorithm works quite well for simple embedded systems because of its low overhead.

Restaurants range from unpretentious lunching or dining places catering to people working nearby, with simple food served in simple settings at low prices, to expensive establishments serving refined food and wines in a formal setting.

A simple electromagnetic relay consists of a coil of wire wrapped around a soft iron core, an iron yoke which provides a low reluctance path for magnetic flux, a movable iron armature, and one or more sets of contacts ( there are two in the relay pictured ).

At a low level, structured programs are often composed of simple, hierarchical program flow structures.

These simple shotguns are often referred to as a " kitchen door gun " or a " farm gun " due to its low cost as a self-defense weapon.

Some simple examples of spinors in low dimensions arise from considering the even-graded subalgebras of the Clifford algebra.

AM demodulation requires the simple rectification of the RF signal ( so-called envelope detection ), and a simple RC low pass filter to remove remnants of the intermediate frequency.

A simple 90 ° V6 with crankshaft counterweights achieves good balance for similar reasons, although the uneven firing intervals will be perceived as roughness at low RPM, making this an unpopular solution.

The exhaust is, however, relatively low in NOx emissions, as combustion temperatures are lower than in other engines, and also because of some inherent Exhaust Gas Recirculation-EGR-in early engines ; the higher the combustion temperature is, the higher the NOx emissions are ( sir Harry Ricardo proved in the 20's that for every 1 % increase of the proportion of exhaust gas in the admission mix, there's a 45º F reduction in flame temperature ); this allowed Mazda to meet the United States Clean Air Act of 1970 in 1973 with a simple and inexpensive ' thermal reactor ' ( an enlarged open chamber in the exhaust manifold ) by paradoxically enriching the air-fuel ratio to the point where the unburned hydrocarbons ( HC ) in the exhaust would support complete combustion in the thermal reactor ; while piston-engine cars required expensive catalytic converters to deal with both unburned hydrocarbons and NOx emissions.

Its combination of low raw material cost, relatively simple processing, and a useful temperature range make it currently the best compromise among the various competing materials.

This is because if a group has sectional 2-rank at least 5 then MacWilliams showed that its Sylow 2-subgroups are connected, and the balance theorem implies that any simple group with connected Sylow 2-subgroups is either of component type or characteristic 2 type.

Its massive contours are rooted in the simple need of man, since he is always incomplete, to complete himself.

Thoroughly modern in treatment, they are at the same time, full of simple sincerity which invariably characterizes genuine Negro folk-music and are by no means to be confused with the average ' Broadway Spirituals ' which depend for their racial flavor upon sundry allusions to the ' Amen Corner ', ' judgement Day, ' Gabriel's Horn, and a frustrated devil -- with a few random hallelujahs thrown in for good measure.

To those of my readers who find many of my opinions morally, or politically, or sociologically antiquated ( and I have reason to know that there are some such ), I would like to say what I have already hinted, namely, that some of my opinions may indeed be subject to some discount on the simple ground that I am no longer young and therefore incapable of being youthful of mind.

Reading, writing and simple arithmetic are taught along with such crafts as working in brass.

It is a simple task to haul a boat fifty or one hundred miles to a lake or reservoir on the new, light, strong, easy-to-operate trailers which are built to accommodate almost any kind of small boat and retail from $100 to $2,000.

They involve only simple mathematics that are taught in grammar school arithmetic classes.

Outputs of the two systems are measured by a pulse-timing circuit and a resistance bridge, followed by a simple analogue computer which feeds a multichannel recorder.

But in a new development where everything starts from scratch the solutions are simple.

We are reporting these investigations here briefly because of their relevancy to problems of the study of apparently simple exchange reactions of chlorine and because the results furnish some information on the activation energy for abstraction of chlorine atoms from carbon tetrachloride.

These are defined by a simple involutorial transformation of the points in which a general line meets a nonsingular quadric surface bearing a curve of symbol Af.

A general line L meets Q in two points, Af and Af, through each of which passes a unique generator of the regulus, Af, whose lines are simple secants of Aj.

If **ya is the multiple secant of **zg which passes through Af and **yb is the simple secant of **zg which passes through Af, and if Af are the points in which **ya meets **zg, and if Af is the image of Af on the generator **yb, it follows that the image of the line Af is Af.

But the symbols he is asked to learn are simple.

In considering roleplaying for analysis we enter a more complex area, since we are now no longer dealing with a simple over-all decision but rather with the examination and evaluation of many elements seen in dynamic functioning.

Since the company under review is supplying what we are here regarding as only one kind of service, we might suppose that the problem of total cost apportionment would be very simple ; ;

`` Purely from the business man's standpoint and without regard to the lawyer's view '', commented a trade journal, `` the matter of patents in the automobile and accessory trade is developing some phases and results that challenge thought as to how far patents are to become weapons of warfare in business, instead of simple beneficient protection devices for encouraging inventive creation ''.

If we have not thought and made a decision entirely in these terms, then we need to submit ourselves to the following `` simple test '': `` Have we decided how we are to kill the other members of our household in the event of our being less injured than they are ''??

Though no longer able to turn out his protoplasmic pen-and-ink sketches ( several old favorites are scattered through the present volume ) Thurber has retained unimpaired his vision of humor as a thing of simple, unaffected humanness.

Algae ( or ; singular alga, Latin for " seaweed ") are a very large and diverse group of simple, typically autotrophic organisms, ranging from unicellular to multicellular forms, such as the giant kelps that grow to 65 meters in length.

Most are photosynthetic like plants, and " simple " because their tissues are not organized into the many distinct organs found in land plants.

Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments ( a multi-variable generalization of simple differences ) differ from the fixed-effects model.

Comparisons, which are most commonly planned, can be either simple or compound.