共查询到20条相似文献,搜索用时 15 毫秒
1.
Egle Bettio Enrico Jabara Bertram A. F. Wehrfritz 《Mediterranean Journal of Mathematics》2014,11(1):1-12
We consider a group G with an automorphism of finite, usually prime, order. If G has finite Hirsch number, and also if G satisfies various stronger rank restrictions, we study the consequences and equivalent hypotheses of having only finitely many fixed-points. In particular we prove that if a group G with finite Hirsch number ${\mathfrak{h}}$ admits an automorphism ${\varphi}$ of prime order p such that ${\vert C_{G}(\varphi) \vert = n < \infty,}$ then G has a subgroup of finite index bounded in terms of p, n and ${\mathfrak{h}}$ that is nilpotent of p-bounded class. 相似文献
2.
Colin D. Reid 《Archiv der Mathematik》2011,96(3):207-214
Let G be a finite non-nilpotent group such that every Sylow subgroup of G is generated by at most δ elements, and such that p is the largest prime dividing |G|. We show that G has a non-nilpotent image G/N, such that N is characteristic and of index bounded by a function of δ and p. This result will be used to prove that G has a nilpotent normal subgroup of index bounded in terms of δ and p. 相似文献
3.
In [2] we proved that ifG is a finite group containing an involution whose centralizer has order bounded by some numberm, thenG contains a nilpotent subgroup of class at most two and index bounded in terms ofm. One of the steps in the proof of that result was to show that ifG is soluble, then ¦G/F(G) ¦ is bounded by a function ofm, where F (G) is the Fitting subgroup ofG. We now show that, in this part of the argument, the involution can be replaced by an arbitrary element of prime order. 相似文献
4.
Antonio Behn 《代数通讯》2013,41(10):4855-4860
Let Gbe a group and let K be a field of characteristic p> 0. If all irreducible representations of the group algebra K[G] have finite degree < n, then we show that G has a subgroup A with |G:A| bounded by a function of nand such that all the irreducible representations of K[A] have degree 1. 相似文献
5.
Aner Shalev 《Israel Journal of Mathematics》1993,82(1-3):395-404
LetG be a finite group admitting an automorphismα withm fixed points. Suppose every subgroup ofG isr-generated. It is shown that (1)G has a characteristic soluble subgroupH whose index is bounded in terms ofm andr, and (2) if the orders ofα andG are coprime, then the derived length ofH is also bounded in terms ofm andr.
To Professor John Thompson, in honor of his outstanding achievements 相似文献
6.
Zu Yun Lu 《数学学报(英文版)》2002,18(2):335-338
Let N be a normal subgroup of a finite group G. Let ϕ be an irreducible Brauer character of N. Assume π is a set of primes and χ(1)/ϕ(1) is a π′-number of any χ∈IBr
p
(G/ϕ). If p∤|G:N|, and N is p-solvable, then G/N has an abelian-by-metabelian Hall-π subgroup; If p∉π then G/N has a metabelian Hall-π subgroup.
Received February 22, 2000, Accepted May 9, 2001 相似文献
7.
A group is said to have finite (special) rank ≤ sif all of its finitely generated subgroups can be generated byselements. LetGbe a locally finite group and suppose thatH/HGhas finite rank for all subgroupsHofG, whereHGdenotes the normal core ofHinG. We prove that thenGhas an abelian normal subgroup whose quotient is of finite rank (Theorem 5). If, in addition, there is a finite numberrbounding all of the ranks ofH/HG, thenGhas an abelian subgroup whose quotient is of finite rank bounded in terms ofronly (Theorem 4). These results are based on analogous theorems on locally finitep-groups, in which case the groupGis also abelian-by-finite (Theorems 2 and 3). 相似文献
8.
Let KG be a group algebra of a finite p-group G over a finite field Kof characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group with a cyclic group of order 4 or G has an abelian subgroup A of index 2 and an element b such that b inverts each element of A. 相似文献
9.
The aim of this paper is to prove that Gn, the subgroup generatedby all nth-powers of a pro-(finite soluble of bounded Fittingheight) group G is a closed subgroup of G 相似文献
10.
I. M. Isaacs 《Archiv der Mathematik》1997,68(5):359-366
Let σ be an automorphism of a finite group G and suppose that σ fixes every element of G that has prime order or order 4. The main result of this paper shows that the structure of the subgroup H=[G, σ] is severely limited in terms of the order n of σ. In particular, H has exponent dividing n and it is nilpotent of class bounded in terms of n. 相似文献
11.
Li Fang WANG Yan Ming WANG 《数学学报(英文版)》2007,23(11):1985-1990
Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result:
If the cyclic subgroups of prime order or order 4 iif p = 2) of every member of З are З-permutable subgroups in G, then G is supersolvable.
In this paper, we give an elementary proof of this theorem and generalize it in terms of formation. 相似文献
12.
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
13.
14.
We give a short proof that if G is a finite group of derived length k and if G admits a fixed-point-free action of the elementary group of order 2 n , then G has a normal series of length n all of whose quotients are nilpotent of class bounded in terms of k and n only. 相似文献
15.
In this paper, we characterize finite groups G satisfying that, for every prime power divisor p n of the order of G, there exists a subgroup H of index p n (of order p n ) in G such that H is normal or abnormal in G. 相似文献
16.
Cutolo G.; Khukhro E. I.; Lennox J. C.; Rinauro S.; Smith H.; Wiegold James 《Bulletin London Mathematical Society》1997,29(5):563-570
For n a positive integer, a group G is called core-n if H/HGhas order at most n for every subgroup H of G (where HG is thenormal core of H, the largest normal subgroup of G containedin H). It is proved that a locally finite core-n group G hasan abelian subgroup whose index in G is bounded in terms ofn. 1991 Mathematics Subject Classification 20D15, 20D60, 20F30. 相似文献
17.
B. A. F. Wehrfritz 《Israel Journal of Mathematics》1984,47(2-3):154-164
LetD=F(G) be a division ring generated as a division ring by its central subfieldF and the polycyclic-by-finite subgroupG of its multiplicative group, letn be a positive integer and letX be a finitely generated subgroup of GL(n, D). It is implicit in recent works of A. I. Lichtman thatX is residually finite. In fact, much more is true. If charD=p≠0, then there is a normal subgroup ofX of finite index that is residually a finitep-group. If charD=0, then there exists a cofinite set π=π(X) of rational primes such that for eachp in π there is a normal subgroup ofX of finite index that is residually a finitep-group. 相似文献
18.
Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):343-348
LetG be a group and ϕ an automorphism ofG. Two elementsx, y ∈ G are called ϕ-conjugate if there existsg ∈ G such thatx=g
−1
yg
θ. It is easily verified that the ϕ-conjugation is an equivalence relation; the numberR(ϕ) of ϕ-classes ofG is called the Reidemeister number of the automorphism ϕ.
In this paper we prove that if a polycyclic groupsG admits an automorphism ϕ of ordern such thatR(ϕ)<∞, thenG contains a subgroup of finite index with derived length at most 2
n−1
.
相似文献
19.
It is known that if a group G has an abelian subgroup of finite index n, then it contains an abelian characteristic subgroup A of index at most nn. The aim of this paper is to improve this bound by showing that the characteristic subgroup A can be chosen of index at most n2. Examples prove that this bound is the best possible. Our main result is obtained as an application of a general method for the construction of large characteristic subgroups. 相似文献
20.
Let G be a finitely generated polyfree group. If G has nonzero Euler characteristic then we show that Aut(G) has a finite index subgroup in which every automorphism has infinite Reidemeister number. For certain G of length 2, we show that the number of Reidemeister classes of every automorphism is infinite. 相似文献