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We consider locally nilpotent periodic groups admitting an almost regular automorphism of order 4. The following are results
are proved: (1) If a locally nilpotent periodic group G admits an automorphism ϕ of order 4 having exactly m<∞ fixed points,
then (a) the subgroup {ie176-1} contains a subgroup of m-bounded index in {ie176-2} which is nilpotent of m-bounded class,
and (b) the group G contains a subgroup V of m-bounded index such that the subgroup {ie176-3} is nilpotent of m-bounded class
(Theorem 1); (2) If a locally nilpotent periodic group G admits an automorphism ϕ of order 4 having exactly m<∞ fixed points,
then it contains a subgroup V of m-bounded index such that, for some m-bounded number f(m), the subgroup {ie176-4}, generated
by all f(m) th powers of elements in {ie176-5} is nilpotent of class ≤3 (Theorem 2).
Supported by RFFR grant No. 94-01-00048 and by ISF grant NQ7000.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 314–333, May–June, 1996. 相似文献
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Let be a graph and let be a group of automorphisms of . The graph is called -normal if is normal in the automorphism group of . Let be a finite non-abelian simple group and let with . In this paper we prove that if every connected pentavalent symmetric -vertex-transitive graph is -normal, then every connected pentavalent symmetric -vertex-transitive graph is -normal. This result, among others, implies that every connected pentavalent symmetric -vertex-transitive graph is -normal except is one of 57 simple groups. Furthermore, every connected pentavalent symmetric -regular graph is -normal except is one of 20 simple groups, and every connected pentavalent -symmetric graph is -normal except is one of 17 simple groups. 相似文献
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Gérard Endimioni 《Journal of Algebra》2010,323(11):3142-3146
A well-known result due to Thompson states that if a finite group G has a fixed-point-free automorphism of prime order, then G is nilpotent. In this note, giving a counterpart of Thompson's result in the context of polycyclic groups, we prove: if a polycyclic group G has an automorphism of prime order with finitely many fixed points, then G is nilpotent-by-finite. 相似文献
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Eric Swartz 《Journal of Combinatorial Theory, Series A》2012,119(5):949-976
In this paper, seven families of vertex-intransitive locally (G,2)-arc transitive graphs are constructed, where Sz(q)?G?Aut(Sz(q)), q=22k+1 for some k∈N. It is then shown that for any graph Γ in one of these families, Sz(q)?Aut(Γ)?Aut(Sz(q)) and that the only locally 2-arc transitive graphs admitting an almost simple group of Suzuki type whose vertices all have valency at least three are (i) graphs in these seven families, (ii) (vertex transitive) 2-arc transitive graphs admitting an almost simple group of Suzuki type, or (iii) double covers of the graphs in (ii). Since the graphs in (ii) have been classified by Fang and Praeger (1999) [6], this completes the classification of locally 2-arc transitive graphs admitting a Suzuki simple group 相似文献
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Linear codes with large automorphism groups are constructed. Most of them are suitable for permutation decoding. In some cases they are also optimal. For instance, we construct an optimal binary code of length \(n=252\) and dimension \(k=12\) having minimum distance \(d=120\) and automorphism group isomorphic to \(\text {PSL}(2,8)\rtimes \text {C}_{3}\). 相似文献
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Let be an almost crystallographic (AC-) group, corresponding to the simply connected, connected, nilpotent Lie group and with holonomy group . If , there is a faithful representation . In case is crystallographic, this condition is known to be equivalent to or . We will show (Example 2.2) that, for AC-groups , this is no longer valid and should be adapted. A generalised equivalent algebraic (and easier to verify) condition is presented (Theorem 2.3). Corresponding to an AC-group and by factoring out subsequent centers we construct a series of AC-groups, which becomes constant after a finite number of terms. Under suitable conditions, this opens a way to represent faithfully in (Theorem 4.1). We show how this can be used to calculate . This is of importance, especially, when is almost Bieberbach and, hence, is known to have an interesting geometric meaning.
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LetX
G,H denote the Cayley graph of a finite groupG with respect to a subsetH. It is well-known that its automorphism groupA(XG,H) must contain the regular subgroupL
G corresponding to the set of left multiplications by elements ofG. This paper is concerned with minimizing the index [A(XG,H)LG] for givenG, in particular when this index is always greater than 1. IfG is abelian but not one of seven exceptional groups, then a Cayley graph ofG exists for which this index is at most 2. Nearly complete results for the generalized dicyclic groups are also obtained. 相似文献
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Journal of Algebraic Combinatorics - Quite a lot of attention has been paid recently to the classification of symmetric Cayley graphs of non-abelian simple groups. Besides the known complete... 相似文献
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N. Yu. Makarenko 《Siberian Mathematical Journal》1994,35(3):564-565
Translated from Sibirskii Matematicheskii, Vol. 35, No. 3, pp. 630–632, May–June, 1994. 相似文献
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Reginaldo M. Marcelo Mari-Jo P. Ruiz Ken-ichi Shinoda 《Graphs and Combinatorics》1994,10(2-4):185-191
In this paper we review the characterization of point-color symmetric (PCS) graphs based on the color preserving automorphisms given in [3]. In particular, we consider PCS pictures, arriving at another characterization theorem. We summarize a few results and give some examples. 相似文献
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ABSTRACT The article is dedicated to some generalizations of minimax soluble groups satisfying common criterion of nilpotency, such that normality of maximal subgroups, nilpotency of the factor-group by the Frattini subgroup, normality of pronormal subgroups, non-existence of proper abnormal subgroups and so on. 相似文献
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For a finite group G, a Cayley graph on G is said to be normal if . In this note, we prove that connected cubic non-symmetric Cayley graphs of the ten finite non-abelian simple groups G in the list of non-normal candidates given in [X.G. Fang, C.H. Li, J. Wang, M.Y. Xu, On cubic Cayley graphs of finite simple groups, Discrete Math. 244 (2002) 67-75] are normal. 相似文献
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S. Foldes 《Algebra Universalis》1999,41(2):115-120
Birkhoff’s theorem that every group is isomorphic to the automorphism group of a distributive lattice is extended in a direction that parallels similar results in graph theory. Received December 9, 1997; accepted in final form October 9, 1998. 相似文献
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We prove that a Minkowski plane with an automorphism group of type 51 is of order 5 and, if it is of type 4 or 7 it is of order 3 or 5.
Received 5 January 1999. 相似文献
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Hou-Yi Chen 《代数通讯》2018,46(6):2693-2695
Let (𝔖n,S) be a Coxeter system of the symmetric group, we show that the set of automorphisms of 𝔖n which are involutions and leave S stable is a finite group of order less than 3. 相似文献