共查询到20条相似文献,搜索用时 15 毫秒
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D. V. Lytkina 《Algebra and Logic》2010,49(3):256-261
We describe {2, 3}-groups without elements of order 27, acting freely on an Abelian group. In particular, it is proved that such groups are locally finite. 相似文献
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Eon-Kyung Lee 《Journal of Pure and Applied Algebra》2011,215(10):2295-2314
Let G be a Garside group with Garside element Δ, and let Δm be the minimal positive central power of Δ. An element g∈G is said to be periodic if some power of it is a power of Δ. In this paper, we study periodic elements in Garside groups and their conjugacy classes.We show that the periodicity of an element does not depend on the choice of a particular Garside structure if and only if the center of G is cyclic; if gk=Δka for some nonzero integer k, then g is conjugate to Δa; every finite subgroup of the quotient group G/〈Δm〉 is cyclic.By a classical theorem of Brouwer, Kerékjártó and Eilenberg, an n-braid is periodic if and only if it is conjugate to a power of one of two specific roots of Δ2. We generalize this to Garside groups by showing that every periodic element is conjugate to a power of a root of Δm.We introduce the notions of slimness and precentrality for periodic elements, and show that the super summit set of a slim, precentral periodic element is closed under any partial cycling. For the conjugacy problem, we may assume the slimness without loss of generality. For the Artin groups of type , , , and the braid group of the complex reflection group of type (e,e,n), endowed with the dual Garside structure, we may further assume the precentrality. 相似文献
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A. N. Ostylovskii 《Mathematical Notes》1986,40(6):906-907
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S. V. Rychkov 《Algebra and Logic》1993,32(2):87-96
Translated fromAlgebra i Logika, Vol. 32, No. 2, pp. 160–176, March–April, 1993. 相似文献
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A. K. Shlyopkin 《Algebra and Logic》1999,38(1):51-66
A group G is saturated with groups in a set X if every finite subgroup of G is embeddable in G into a subgroup L isomorphic
to some group in X. We show that a Shunkov group has a periodic part if the saturating set for it coincides with one of the
following: {L2(q)}, {Sz(q)}, {Re(q)}, or {U3(2n)}.
Translated fromAlgebra i Logika, Vol. 38, No. 1, pp. 96–125, January–February, 1999. 相似文献
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We consider certain properties of *-wild groups and prove that periodic groups are not *-wild. 相似文献
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B. Nagy 《Proceedings of the American Mathematical Society》1998,126(5):1433-1444
Spectral operators of scalar type in the sense of Dunford often occur in connection with unconditionally convergent series expansions, whereas conditionally convergent expansions under similar conditions may be described with the help of operators having a more general type of spectral decomposition. We show that under certain conditions even in the latter case we can restrict our considerations to a dense linear submanifold of the original Banach space with a stronger topology, where the convergence of the expansion under study will be unconditional. Though our conditions could be formulated in terms of a single operator, it seems to be more natural to state them in terms of (the generator of) a periodic group of operators.
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Automorphism groups of semidirect products 总被引:1,自引:0,他引:1
This paper shows that if is a semidirect product of finite groups, then if and only if and for all . As an application, we investigate the automorphism group of a split metacyclic p-group for odd p.
The second author is supported by the Natural Science Foundation of China (10671058). 相似文献
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