Примеры использования Maximal subgroups на Английском языке и их переводы на Русский язык
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There are 9 conjugacy classes of maximal subgroups of J2.
Maximal subgroups in the theory of finite group classes, Minsk, Belarus.
Finite groups with given generalized maximal subgroups.
A 168-subgroup has 14 maximal subgroups of order 24, isomorphic to S4.
Ona finite groups with the restricted indices of maximal subgroups/ V.S.
First they show that the maximal subgroups of type I are all Frobenius groups.
So the primes dividing the order of G are partitioned into equivalence classes corresponding to the conjugacy classes of maximal subgroups.
Originally the theorem was about maximal subgroups of the symmetric group.
The Hall-Janko graph can be constructed out of objects in U3(3), the simple group of order 6048: In U3(3)there are 36 simple maximal subgroups of order 168.
Finite groups with generalized P-subnormal second maximal subgroups// Asian-European Journal of Mathematics.
Two maximal subgroups are conjugate if and only if the sets σ(M) are the same, and if they are not conjugate then the sets σ(M) are disjoint.
Both of the two types of stabilizers are maximal subgroups of the whole automorphism group of the Hoffman-Singleton graph.
Analysis of this type requires knowing about the possible primitive actions of almost simple groups,which is equivalent to knowing the maximal subgroups of almost simple groups.
On an influence of indices of maximal subgroups on nilpotent length of finite soluble groups/ V.S.
However, in the proof of the odd-order theorem, the arguments for constructing characters of G from characters of subgroups are far more delicate, anduse the Dade isometry between character rings rather than character induction, since the maximal subgroups have a more complicated structure and are embedded in a less transparent way.
Influence X-permutable of the maximal subgroups of Sylow's and Hall's subgroups with the allocated subgroups on a structure of finite group is investigated.
This pattern of partitioning the prime divisors of|G| according to conjugacy classes of certain Hall subgroups(a Hall subgroup is one whose order and index are relatively prime)which correspond to the maximal subgroups of G(up to conjugacy) is repeated in both the proof of the Feit-Hall-Thompson CN-theorem and in the proof of the Feit-Thompson odd-order theorem.
If all maximal subgroups are type I then an argument similar to the CN case shows that the group G cannot be an odd-order minimal simple group, so there are exactly two classes of maximal subgroups of types II, III, IV or V. Most of the rest of the proof now focuses on these two types of maximal subgroup S and T and the relation between them.
Wilson(1984) and Tchakerian(1986) independently found the 8 classes of maximal subgroups of the Tits group as follows: L3(3): 2 Two classes, fused by an outer automorphism.
All but two classes of maximal subgroups are of type I, but there may also be two extra classes of maximal subgroups, one of type II, and one of type II, III, IV, or V. If X is an irreducible character of the normalizer H of the maximal abelian subgroup A of the CA group G, not containing A in its kernel, we can induce X to a character Y of G, which is not necessarily irreducible.
The structure of a finite group is closely linked to conditions imposed on the maximal subgroups, Sylow subgroups of the group or the Sylow subgroups of some selected subgroups of the group.
Whereas in the CN-case,the resulting maximal subgroups M are still Frobenius groups, the maximal subgroups that occur in the proof of the odd-order theorem need no longer have this structure, and the analysis of their structure and interplay produces 5 possible types of maximal subgroups, called types I, II, III, IV, V. Type I subgroups are of"Frobenius type", a slight generalization of Frobenius group, and in fact later on in the proof are shown to be Frobenius groups.
The Tits group occurs as a maximal subgroup of the Fischer group Fi22.
M12 has a simple subgroup of order 660, a maximal subgroup.
The groups 2F4(2)also occurs as a maximal subgroup of the Rudvalis group, as the point stabilizer of the rank-3 permutation action on 4060 1+ 1755+ 2304 points.
Each maximal subgroup M has a certain nilpotent Hall subgroup Mσ with normalizer contained in M, whose order is divisible by certain primes forming a set σM.
An image of a dodecad has a centralizer of type 211:M12:2,which is contained in a maximal subgroup of type 211:M24.
An image of an octad or16-set has a centralizer of the form 21+8. O8+(2), a maximal subgroup.
In particular, we describe the structure of a Schmidt groups in which every maximal subgroup(generalized) permutes with every 4-maximal subgroup, or every 2-maximal subgroup(generalized) permutes with every 4-maximal subgroup. .
Suppose that either every maximal subgroup of P or every cyclic subgroup of P with order p and with order 4(if P is a non-abelian 2-group) not having a supersoluble supplement in G is weakly quasinormal in G.