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This work was supported by the DFG and by a Polish grant BW/5100-5-0116-3. 相似文献
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On automorphism groups of some finite groups 总被引:1,自引:0,他引:1
钱国华 《中国科学A辑(英文版)》2003,46(4):450-458
We show that if n > 1 is odd and has no divisor p4 for any prime p, then there is no finite group G such that│Aut(G)│ = n. 相似文献
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Yann Ollivier Daniel T. Wise 《Transactions of the American Mathematical Society》2007,359(5):1959-1976
For each countable group we produce a short exact sequence where has a graphical presentation and is f.g. and satisfies property .
As a consequence we produce a group with property such that is infinite.
Using the tools developed we are also able to produce examples of non-Hopfian and non-coHopfian groups with property .
One of our main tools is the use of random groups to achieve certain properties.
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Let G be a finite group and Out Col(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether OutCol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol(G) to be a p′-group are obtained. Our results generalize some well-known theorems. 相似文献
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Julien Bichon 《Proceedings of the American Mathematical Society》2003,131(3):665-673
A quantum analogue of the automorphism group of a finite graph is introduced. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group .
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S. Marshall 《Journal of Graph Theory》2002,41(3):238-248
It was shown by Babai and Imrich [2] that every finite group of odd order except and admits a regular representation as the automorphism group of a tournament. Here, we show that for k ≥ 3, every finite group whose order is relatively prime to and strictly larger than k admits a regular representation as the automorphism group of a k‐tournament. Our constructions are elementary, suggesting that the problem is significantly simpler for k‐tournaments than for binary tournaments. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 238–248, 2002 相似文献
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Groups are classified whose automorphism group is minimal non-nilpotent.The first author wishes to thank the Mathematics Department of Napoli for its warm hospitality for the time of writing this paper. 相似文献
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If \(A\) is a nontrivial torsion-free, locally cyclic group with no nontrivial divisible quotients, and \(G\) is the split extension of \(A\) by a group of order 2 acting on \(A\) by means of the inverting map, then \(G\simeq {{{\mathrm{Aut}}}G} \). We prove that in no other case the full automorphism group of a group is infinite and locally dihedral. 相似文献
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Let S be a finite linear space, and letG be a group of automorphisms of S. IfG is soluble and line-transitive, then for a givenk but a finite number of pairs of (S, G),S hasv= p
n
points andG ⩽AΓL(1,p
n
). 相似文献