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1.
In this paper, it is proved that the simple orthogonal groups O
2n+1(q) and O
2n
±
(q) (where q is odd) cannot be automorphism groups of finite left distributive quasigroups. This is a particular case of the conjecture stating that the automorphism group of a left distributive quasigroup is solvable. To complete the proof of the conjecture, one must test all finite groups. 相似文献
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An automorphism α of a group G is called a noetherian automorphism if for each ascending chain
of subgroups of G there is a positive integer m such that
for all n ≥ m. The structure of the group of all noetherian automorphisms of a group is investigated in this paper. 相似文献
5.
Zahedeh Azhdari 《代数通讯》2013,41(10):4133-4139
Let G be a group and Autc(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Autc(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic and Inn(G) < C* = Autc(G). In this article, we characterize all finitely generated groups G for which the equality Autc(G) = Inn(G) holds. 相似文献
6.
二秩无扭群的自同构群和只有两个自同构的二秩无扭群 总被引:1,自引:0,他引:1
本文利用Kurǒs不变量理论和不定方程理论,讨论了二秩无扭群的自同构群,以及有零高元的二秩无扭群只有两个自同构的充要条件. 相似文献
7.
D. V. Ovchinnikov 《Algebra and Logic》2014,53(2):133-139
8.
Young Jo Kwak 《代数通讯》2013,41(5):2099-2106
Let (V, Q) be a quadratic vector space over a fixed field. Orthogonal group 𝒪(V, Q) is defined as automorphisms on (V, Q). If Q = I, it is 𝒪(V, I) = 𝒪(n). There is a nice result that 𝒪(n) ? Aut(𝔬(n)) over ? or ?, where 𝔬(n) is the Lie algebra of n × n alternating matrices over the field. How about another field The answer is “Yes” if it is GF(2). We show it explicitly with the combinatorial basis ?. This is a verification of Steinberg's main result in 1961, that is, Aut(𝔬(n)) is simple over the square field, with a nonsimple exception Aut(𝔬(5)) ? 𝒪(5) ? 𝔖6. 相似文献
9.
Jiří Rachůnek 《Order》2001,18(4):349-357
By the Holland Representation Theorem, every lattice ordered group (l-group) is isomorphic to a subalgebra of the l-group of automorphisms of a chain. Since weakly associative lattice groups (wal-groups) and tournaments are non-transitive generalizations of l-groups and chains, respectively, the problem concerning the possibility of representation of wal-groups by automorphisms of tournaments arises. In the paper we describe the class of wal-groups isomorphic to wal-groups of automorphisms of tournament and show some of its properties. 相似文献
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Mathematical Notes - 相似文献
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Using the canonical JSJ splitting, we describe the outer automorphism group Out(G) of a one-ended word hyperbolic group G. In particular, we discuss to what extent Out(G) is virtually a direct product of mapping class groups and a free abelian group, and we determine for which groups Out(G) is infinite. We also show that there are only finitely many conjugacy classes of torsion elements in Out(G), for G any torsion-free hyperbolic group. More generally, let Γ be a finite graph of groups decomposition of an arbitrary group G such that edge groups Ge are rigid (i.e. Out(Ge) is finite). We describe the group of automorphisms of G preserving Γ, by comparing it to direct products of suitably defined mapping class groups of vertex groups. 相似文献
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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
16.
Martin Hertweck 《Monatshefte für Mathematik》2002,242(2):1-7
Let G be a finite group whose Sylow 2-subgroups are either cyclic, dihedral, or generalized quaternion. It is shown that a class-preserving automorphism of G of order a power of 2 whose restriction to any Sylow subgroup of G equals the restriction of some inner automorphism of G is necessarily an inner automorphism. Interest in such automorphisms arose from the study of the isomorphism problem for integral group rings, see [6, 7, 13, 14]. 相似文献
17.
In this article we consider groups of automorphisms of flnite linear spaces that act prindtivelyon the lines. A finite linear space S consists of a set P of v points, together with a set L of bdistinguished subsets of P called lines, such that any two points lie on exactly one line. Supposethat a finite Iinear space S has a line-transitive subgroup, G, of automorphisms. Then everyline has the same number k of points and we call such a lineax space a regular linear space or a2 - (v, k, 1) de… 相似文献
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本文得到有限循环群的完全同构基数的一个计算公式 ,并给出有限 Abel群的一个同态为完全同构的一个充要条件 . 相似文献
19.
V. L. Popov 《Doklady Mathematics》2018,98(2):413-415
The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established. 相似文献
20.
Martin Hertweck 《Monatshefte für Mathematik》2002,136(1):1-7
Let G be a finite group whose Sylow 2-subgroups are either cyclic, dihedral, or generalized quaternion. It is shown that a class-preserving
automorphism of G of order a power of 2 whose restriction to any Sylow subgroup of G equals the restriction of some inner automorphism of G is necessarily an inner automorphism. Interest in such automorphisms arose from the study of the isomorphism problem for
integral group rings, see [6, 7, 13, 14].
Received 30 September 2001; in revised form 10 December 2001 相似文献