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Page "Classification of finite simple groups" ¶ 25
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group and is
The content is not the same, however: rather than individual security, it is the security and continuing existence of an `` ideological group '' -- those in the `` free world '' -- that is basic.
Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.
The music director of the Pittsburgh Symphony Orchestra, William Steinberg, has molded his group into a prominent musical organization, which is his life.
With the group of boys it is different.
Nothing is more revealing of the way of life and literary aspirations of this group than their attitude toward sex.
This group is secularist and their program tends to be technological.
But the problem is one which gives us the measure of a man, rather than a group of men, whether a group of doctors, a group of party members assembled at a dinner to give their opinion, or the masses of the voters.
The group conducting the review is not holding formal hearings.
After allowing for group exposures, it is apparent that other factors must be considered if we are to comprehend fanaticism.
At Sounion there is a group of beautiful columns, the ruins of a temple to Poseidon, of particular interest at that time, as active reconstruction was in progress.
He is uncompromising in assigning guilt to the man who finds it necessary to inflict or permit injury to one individual or group for the sake of a larger good.
In the main stream of historical thinking is a group of scholars, H.M. Chadwick, R.H. Hodgkin, Sir Frank Stenton et al. who are in varying degrees sceptical of the native traditions of the conquest but who defend the catastrophic type of invasion suggested by them.
Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.
Patchen's musicians are outsiders in established jazz circles, and Patchen himself has remained outside the San Francisco poetry group, maintaining a self-imposed isolation, even though his conversion to poetry-and-jazz is not as extreme or as sudden as it may first appear.
Gov. Dalton's New Commerce and Industry Commission is moving to create a nine-state regional group in a collective effort to attract new industry.
Fortunately, there is a nursery school which he has been able to attend, with a group of normal children.
Perhaps Khrushchev is in a more difficult position than any since 1957, when the `` anti-party group '' nearly liquidated him.
When the fate of the individual is visited on the group, then ( the warm sweet butter dripped from her raised trembling fork and she pushed her head forward belligerently ), ah, then the true bitterness of existence could be tasted.
Mr. Claude is a specialist in torso development and he has long favored the now-famous Weider Push-Pull Super-Set technique in which one exercise of the Super-Set is a pressing or `` pushing '' movement which accents one sector of a muscle group in a specific way, followed by a `` pulling '' exercise which works the opposing sector of the same muscle group.

group and characteristic
Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.
-- The crystallization of copolymers comprising Af units interspersed with a minor percentage of Af is limited by the inability of the crystal lattice characteristic of the former to accommodate the bulky side group of the latter.
Their characteristic experience is that of the individual at an altar or a shrine rather than that of a continuing social group with a distinctive kind of fellowship.
Some alkaloids do not have the carbon skeleton characteristic of their group.
In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.
Examples of characteristic subgroups include the commutator subgroup and the center of a group.
A characteristic subgroup of a group G is a subgroup H that is invariant under each automorphism of G. That is,
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.
Their classification is divided into the small and large rank cases, where the rank is the largest rank of an odd abelian subgroup normalizing a nontrivial 2-subgroup, which is often ( but not always ) the same as the rank of a Cartan subalgebra when the group is a group of Lie type in characteristic 2.
If a group has an involution with a 2-component that is a group of Lie type of odd characteristic, the goal is to show that it has a centralizer of involution in " standard form " meaning that a centralizer of involution has a component that is of Lie type in odd characteristic and also has a centralizer of 2-rank 1.
The problem is to show that if a group has a centralizer of involution in " standard form " then it is a group of Lie type of odd characteristic.
A quasithin group is one whose 2-local subgroups have p-rank at most 2 for all odd primes p, and the problem is to classify the simple ones of characteristic 2 type.
One usage refers to a variety of a language that is a characteristic of a particular group of the language's speakers.
Provided the sample size is adequate, the risks associated with random allocation ( such as failing to obtain a representative sample in a survey, or having a serious imbalance in a key characteristic between a treatment group and a control group ) are calculable and hence can be managed down to an acceptable level.
If the graph G is connected, then the rank of the free group is equal to 1 − χ ( G ): one minus the Euler characteristic of G.
If the field of scalars of the vector space has characteristic p, and if p divides the order of the group, then this is called modular representation theory ; this special case has very different properties.

group and 2
This was particularly noticeable in group A and group B sera, in which cases activity in Regions 1 and 2 was usually not detectable without prior concentration and occasionally could not be detected at all.
There appeared to be no difference in the distribution of anti-A and anti-B activity in group O serum, though in two group O donors ( J. F. and E. M. ) only one type of agglutinin was found in the regions of low anionic binding capacity ( Figs. 1 and 2 ).
A sample of Fraction Af from group O plasma was dissolved in starting buffer, dialyzed against this buffer and subjected to chromatography using the gradient shown in Fig. 2.
Not until the group was satisfied in this area were they willing to venture further to ( 2 ), Specific adjustment areas, such as sex, in-laws, religion, finance, and so on.
Figure 2 is a graph of the mean achievement scores of each group.
The American Standard Code for Information Interchange ( ASCII ) was developed under the auspices of a committee of the American Standards Association, called the X3 committee, by its X3. 2 ( later X3L2 ) subcommittee, and later by that subcommittee's X3. 2. 4 working group.
The X3. 2. 4 task group voted its approval for the change to ASCII at its May 1963 meeting.
Antimony is in the nitrogen group ( group 15 ) and has an electronegativity of 2. 05.
It lacks the NH < sub > 2 </ sub > group because of the cyclization of the side-chain and is known as an imino acid ; it falls under the category of special structured amino acids .</ ref > where R is an organic substituent known as a " side-chain "); often the term " amino acid " is used to refer specifically to these.
At pH values greater than the pKa of the carboxylic acid group ( mean for the 20 common amino acids is about 2. 2, see the table of amino acid structures above ), the negative carboxylate ion predominates.
Thus, at pH between 2. 2 and 9. 4, the predominant form adopted by α-amino acids contains a negative carboxylate and a positive α-ammonium group, as shown in structure ( 2 ) on the right, so has net zero charge.
Below pH 2. 2, the predominant form will have a neutral carboxylic acid group and a positive α-ammonium ion ( net charge + 1 ), and above pH 9. 4, a negative carboxylate and neutral α-amino group ( net charge − 1 ).
An amide is a compound with the functional group R < sub > n </ sub > E ( O )< sub > x </ sub > NR '< sub > 2 </ sub > ( R and R ' refer to H or organic groups ).
The term amide refers both to classes of compounds and to the functional group ( R < sub > n </ sub > E ( O )< sub > x </ sub > NR '< sub > 2 </ sub >) within those compounds.
One is an amino group, — NH < sub > 2 </ sub >, and one is a carboxylic acid group, — COOH ( although these exist as — NH < sub > 3 </ sub >< sup >+</ sup > and — COO < sup >−</ sup > under physiologic conditions ).

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