共查询到20条相似文献,搜索用时 15 毫秒
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By studying the group of self homotopy equivalences of the localization (at a prime p and/or zero) of some aspherical complexes, we show that, contrary to the case when the considered space is a nilpotent, ?m #(Xp ) is in general different from ?m #(X)p. That is the case even when X = K (G, 1) is a finite complex and/or G satisfies extra finiteness or nilpotency conditions, for instance, when G is finite or virtually nilpotent. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Hans Joachim Baues 《Transactions of the American Mathematical Society》1996,348(12):4737-4773
We consider the group of homotopy equivalences of a simply connected manifold which is part of the fundamental extension of groups due to Barcus-Barratt. We show that the kernel of this extension is always a finite group and we compute this kernel for various examples. This leads to computations of the group for special manifolds , for example if is a connected sum of products of spheres. In particular the group is determined completely. Also the connection of with the group of isotopy classes of diffeomorphisms of is studied.
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We investigate the group of self homotopy equivalences of a space X which induce the identity homomorphism on all homotopy groups. We obtain results on the structure of provided the p-localization of X has the homotopy type of a p-local product of odd-dimensional spheres. In particular, we show that is a semidirect product of certain homotopy groups . We also show that has a central series whose successive quotients are , which are direct sums of homotopy groups of p-local spheres. This leads to a determination of the order of the p-torsion subgroup of and an upper bound for its p-exponent. These results apply to any Lie group G at a regular prime p. We derive some general properties of and give numerous explicit calculations.
Received: 14 April 2001; in final form: 10 September 2001 / Published online: 17 June 2002 相似文献
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1179–1183, September, 1989. 相似文献
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LetG be a finitep-group, and letU(G) be the group of units of the group algebraFG, whereF is a field of characteristicp. It is shown that, if the commutative subgroup ofG has order at leastp
2, then the nilpotency class ofU(G) is at least 2p−1.
The authors are grateful to the Dipartimento di Matematica of the Universita di Trento, and to the Mathematical Institute
of the University of Oxford, for their hospitality while this paper was being written. Then are also grateful to Robert Sandling,
for communication of results, and problems, prior to publication. 相似文献
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XIAJIANGUO 《高校应用数学学报(英文版)》1998,13(1):109-116
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal sub-group of G. For principal fibre bundle (E,p, E,/G;G) tmd (E/H,p‘,E/G;G/H), the relation between auta(E) (resp. autce (E)) and autG/H(E/H) (resp. autGe/H(E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group JG(E) (resp. SG(E)) while the group J G/u(E/H) is known. 相似文献
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Aner Shalev 《Israel Journal of Mathematics》1990,70(3):257-266
The nilpotency class of the unit groupU of a modularp-group algebraFG is determined whenp is odd andG has a cyclic commutator subgroup. This is done via an extension of a theorem of Coleman and Passman, dealing with wreath
products obtained as sections ofU. 相似文献
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Kai Xu 《Israel Journal of Mathematics》1996,93(1):189-194
LetX be a finitep-torsion based connected nilpotent CW-complex. We give a criterion of a subgroup of ε(X), the group of self equivalences ofX, to be a nilpotent group, in terms of its action onE
*(X), whereE is a CW-spectrum, satisfying some technical conditions. 相似文献
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In this paper, we study subgroups of self-homotopy equivalences associated to generalized homology theories. We generalize
Dror-Zabrodsky’s nilpotency theorem on the group of self-homotopy equivalences.
Dedicated to Professor Akio Hattori on his sixtieth birthday
The first-named author was partially supported by Grant-in-Aid for the Science Research of the Ministry of Education, 02740012. 相似文献
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A. B. Konovalov 《Ukrainian Mathematical Journal》1995,47(1):42-49
It is proved that the wreath product of a second-order group and the commutant of a dihedral group is imbedded into a multiplicative group of a modular group algebra of a dihedral group of order 2
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. This implies that the nilpotency class of the multiplicative group is equal to 2
n–2, i.e., to the order of the commutant of the dihedral group.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 39–45, January, 1995. 相似文献