共查询到20条相似文献,搜索用时 15 毫秒
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B.A.F. Wehrfritz 《Journal of Pure and Applied Algebra》2011,215(5):1112-1115
Suppose G is either a soluble (torsion-free)-by-finite group of finite rank or a soluble linear group over a finite extension field of the rational numbers. We consider the implications for G if G has an automorphism of finite order m with only finitely many fixed points. For example, if m is prime then G is a finite extension of a nilpotent group and if m=4 then G is a finite extension of a centre-by-metabelian group. This extends the special cases where G is polycyclic, proved recently by Endimioni (2010); see [3]. 相似文献
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B. A. F. Wehrfritz 《Rendiconti del Circolo Matematico di Palermo》2011,60(3):365-370
Let φ be an automorphism of order 2 of the group G with C G (φ) finite. We prove the following. If G has finite Hirsch number then G is (nilpotent of class at most 2)-by-finite but need not be abelian-by-finite. If G is a finite extension of a soluble group with finite abelian ranks, then G is abelian-by-finite. 相似文献
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Bertram A.F. Wehrfritz 《Central European Journal of Mathematics》2011,9(3):616-626
Let ϕ be an automorphism of prime order p of the group G with C
G
(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are bounded in terms of p, n and h only. Here a group has finite Hirsch number if it is poly (cyclic or locally finite). This is a stronger notion than that
used in [Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)], where the
case p = 2 is discussed. 相似文献
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E. I. Khukhro 《Mathematical Notes》1978,23(5):359-362
It is proved that if a finite group admits a fixed-point-free automorphism of order 2n, then its nilpotent length is at most n. It had been proved by Gross [1] that its nilpotent length is at most 2n–2.Translated from Matematicheskie Zametki, Vol. 23, No. 5, pp. 651–657, May, 1978. 相似文献
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Peter Rowley 《Israel Journal of Mathematics》1985,51(1-2):125-150
This paper, which is one of a series of four, contributes to the proof of the following
Theorem.A finite group admitting a coprime fixed-point-free automorphism α of order rst (r, s andt distinct primes)is soluble.
Here we prove that in a minimal counterexample to the above theorem the set ofα-invariant Sylowp-subgroupsP, such thatC
p(α
i)≠1 for allα
i≠1, generate a soluble subgroup. 相似文献
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E. I. Khukhro 《Algebra and Logic》2011,49(6):551-560
Suppose that a finite group G admits a Frobenius group FH of automorphisms with kernel F and complement H such that the fixed-point subgroup of F is trivial, i.e., CG(F) = 1, and the orders of G and H are coprime. It is proved that the nilpotent length of G is equal to the nilpotent length of CG(H) and the Fitting series of the fixed-point subgroup CG(H) coincides with a series obtained by taking intersections of CG(H) with the Fitting series of G. 相似文献
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I. Kh. Bekker 《Mathematical Notes》1997,61(4):399-408
In the paper, sufficient conditions for the splittability of mixed Abelian groups with periodic automorphism groups are established.
Classes of mixed splittable Abelian groups with perfect holomorphs are distinguished.
Translated fromMaternaticheskie Zametki, Vol. 61, No. 4, pp. 483–493, April, 1997.
Translated by A. I. Shtern 相似文献
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Enrico Jabara 《Journal of Algebra》2010,323(10):2798-2817
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In this paper we describe all abelian groups which can be expanded as the direct product of cyclic subgroups which have regular automorphisms of given prime order and also find the necessary and sufficient conditions for the existence of regular semiautomorphisms of prime order for metabelian groups the orders of the elements of which are bounded as a set.Translated from Matematicheskie Zametki, Vol. 12, No. 6, pp. 727–738, December, 1972. 相似文献
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n this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map φ: G → G defined by gφ = [g,α] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H″ is included in the centre of H and CH(α2) is abelian, both CG(α2) and G/[G, α2] are abelian-by-finite. These results extend recent and classical results in the literature. 相似文献