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1.
We prove that a finite group whose every maximal subgroup is simple or nilpotent is a Schmidt group. A group whose every maximal subgroup is simple or supersoluble can be nonsoluble, and in this case we prove that its chief series has the form 1 ? K ? G, K }~ PSL 2(p) for a suitable prime p, |G: K| ≤ 2. 相似文献
2.
The spectrum of a group is the set of its element orders. Let L = PSL n (q), where n is a prime greater than 3. We show that every finite group whose spectrum is the same as the spectrum of L is isomorphic to an extension of L by a subgroup of the outer automorphism group of L. 相似文献
3.
There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J1×J1×L2(19), where J1 is the first Janko group, of order 175560, and L2(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective polytopes of type {5, 3, 5} must in turn cover this one. 相似文献
4.
Let Ra denote the half turn about the point a of the hyperbolic plane H. If the points a, b, c, d lie on the same line and the pair (c, d) is obtained from the pair (a, b) by a translation, then we have RaRb = RcRd. We study the group G whose generating set is {Ra:a∈H} and whose defining relations are the ones mentioned above together with the relations R2a = 1. We show that G can be made into a Lie group, G has two connected components, and its identity component G0 is the universal covering group of PSL2(R). In particular, it follows that all relations between the half turns in PSL2(R) follow from the abovementioned relations and a single additional relation of length five. 相似文献
5.
SupposeD is a division algebra of degreep over its centerF, which contains a primitivep-root of 1. Also supposeD has a maximal separable subfield overF whose Galois group is the semidirect product of the cyclic groupsC p C q , whereq=2, 3, 4, or 6 and is relatively prime top (In particular this is the case whenp is prime ≤7 andD has a maximal separable subfield whose Galois group is solvable.) ThenD is cyclic. The proof involves developing a theory of a wider class of algebras, which we call accessible, and proving that they are cyclic. 相似文献
6.
Jonathan Ariel Barmak 《Discrete Mathematics》2009,309(10):3424-3426
For any finite group G, we construct a finite poset (or equivalently, a finite T0-space) X, whose group of automorphisms is isomorphic to G. If the order of the group is n and it has r generators, X has n(r+2) points. This construction improves previous results by G. Birkhoff and M.C. Thornton. The relationship between automorphisms and homotopy types is also analyzed. 相似文献
7.
A. Mouhib 《Journal of Number Theory》2009,129(6):1205-1211
This paper investigates the 2-class group of real multiquadratic number fields. Let p1,p2,…,pn be distinct primes and . We draw a list of all fields K whose 2-class group is trivial. 相似文献
8.
Peter Köhler Thomas Meixner Michael Wester 《Journal of Combinatorial Theory, Series A》1985,38(2):203-209
A certain “free” group U is constructed that is generated by three elements of order 3 which pairwise generate a Frobenius group of order 21 and it is shown that U operates regularly on the affine building of type over the field of 2-adic numbers. As a result an infinite series of finite rank 3 geometries is obtained whose rank 2 residues are projective planes of order 2, and which possess a regular automorphism group isomorphic to SL3(p) or SU3(p) for some prime p. 相似文献
9.
We consider a family of motives associated to the rigid local system whose monodromy is dense in the simple algebraic group of type G2 and which has a local monodromy of order 7 at ∞. We prove an explicit Hilbert irreduciblity theorem for the associated étale realizations and deduce that the specialized motives at the points of irreducibility have motivic Galois group G2. 相似文献
10.
N. V. Maslova 《Proceedings of the Steklov Institute of Mathematics》2016,295(1):109-119
Let G be a finite group. The set of all prime divisors of the order of G is called the prime spectrum of G and is denoted by π(G). A group G is called prime spectrum minimal if π(G) ≠ π(H) for any proper subgroup H of G. We prove that every prime spectrum minimal group all of whose nonabelian composition factors are isomorphic to the groups from the set {PSL 2(7), PSL 2(11), PSL 5(2)} is generated by two conjugate elements. Thus, we extend the corresponding result for finite groups with Hall maximal subgroups. Moreover, we study the normal structure of a finite prime spectrum minimal group with a nonabelian composition factor whose order is divisible by exactly three different primes. 相似文献
11.
Du et al. (in J. Comb. Theory B 74:276–290, 1998 and J. Comb. Theory B 93:73–93, 2005), classified regular covers of complete graph whose fiber-preserving automorphism group acts 2-arc-transitively, and whose covering transformation group is either cyclic or isomorphic to $\mathbb{Z}_{p}^{2}$ or $\mathbb{Z}_{p}^{3}$ with p a prime. In this paper, a complete classification is achieved of all the regular covers of bipartite complete graphs minus a matching K n,n ?nK 2 with cyclic covering transformation groups, whose fiber-preserving automorphism groups act 2-arc-transitively. 相似文献
12.
A finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N G (〈x〉)/C G (〈x〉) ≌ Aut(〈x〉) for every x ∈ G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups. 相似文献
13.
Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z2, where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D4 is the Cherednik algebra of type C∨C1, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI. 相似文献
14.
For a family of group words w we show that if G is a profinite group in which all w-values are contained in a union of finitely many subgroups with a prescribed property, then the verbal subgroup w(G) has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank. If G contains finitely many subgroups G 1, G 2, . . . , G s of finite exponent e whose union contains all γ k -values in G, it is shown that γ k (G) has finite (e, k, s)-bounded exponent. If G contains finitely many subgroups G 1, G 2, . . . , G s of finite rank r whose union contains all γ k -values, it is shown that γ k (G) has finite (k, r, s)-bounded rank. 相似文献
15.
M. Chaboksavar M. Farrokhi Derakhshandeh Ghouchan F. Saeedi 《Archiv der Mathematik》2014,102(5):401-409
Let G be a group and L(G) be the absolute center of G, that is, the set of all elements of G fixed by all automorphisms of G. In this paper, we classify all finite groups G whose absolute central factors are isomorphic to a cyclic group, \({\mathbb{Z}_p \times \mathbb{Z}_p}\) , D 8, Q 8, or a non-abelian group of order pq for some distinct primes p and q. 相似文献
16.
Eric K. van Douwen 《Algebra Universalis》1980,11(1):389-392
It is consistent withZFC+¬CH that there is a Boolean algebra of cardinality ω1 whose automorphism group is countably infinite. This answers a question of McKenzie and Monk. 相似文献
17.
Kichi-Suke Saito 《Journal of Functional Analysis》1982,45(2):177-193
Let G be a compact abelian group with the archimedean totally ordered dual Γ and let be the von Neumann algebra crossed product determined by a finite von Neumann algebra M and a one-parameter group {αγ}γ?Γ of trace preserving 1-automorphisms of M. In this paper, we investigate the structure of invariant subspaces and cocycles for the subalgebra + of consisting of those operators whose spectrum with respect to the dual automorphism group {βg}g?G on is nonnegative. Our main result asserts that if M is a factor, then + is maximal among the σ-weakly closed subalgebras of . 相似文献
18.
If G is a countable, discrete group generated by two finite subgroups H and K and P is a II1 factor with an outer G-action, one can construct the group-type subfactor PH⊂P?K introduced by Haagerup and the first author to obtain numerous examples of infinite depth subfactors whose standard invariant has exotic growth properties. We compute the planar algebra of this subfactor and prove that any subfactor with an abstract planar algebra of “group type” arises from such a subfactor. The action of Jones' planar operad is determined explicitly. 相似文献
19.
A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2015,289(1):139-145
It is proved that the groups E 7(2) and E 7(3) are recognizable by their prime graphs. As a corollary, this completes the proof of V.D. Mazurov’s conjecture that every finite simple group whose prime graph has at least three connected components is either recognizable by spectrum or isomorphic to A 6. 相似文献
20.
Roe Goodman 《Journal of Functional Analysis》1979,31(1):115-137
Let G be a connected, simply-connected complex nilpotent Lie group, and Gr ?( G a real form of G. Motivated by the problem of analytic continuation of Banach-space representations of GR to holomorphic representations of G, we construct translation-invariant locally-convex algebras of entire functions on G (generalizing the classical spaces of entire functions of finite exponential order). The dual spaces of these algebras are naturally identified with algebras of left-invariant differential operators of infinite order on G. In connection with analytic continuation of unitary representations of GR, we study the convex cone of entire functions on G whose restrictions to GR are positive-definite, and determine the minimal order of growth at infinity of such functions. 相似文献