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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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In this article, the question is considered whether there exist finite translation planes with arbitrarily small kernels admitting nonsolvable collineation groups. For any integerN, it is shown that there exist translation planes of dimension >N and orderq 3 admittingGL(2,q) as a collineation group.  相似文献   

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We take a further step toward the classification of all flat (2-dimensional) Laguerre planes of group dimension 4 by determining, up to isomorphism, all such Laguerre planes that admit 4-dimensional groups of automorphisms that fix at least two parallel classes. It is shown that these planes occur among those flat Laguerre planes of generalised shear type that admit a 3-dimesional kernel.  相似文献   

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We investigate methods for constructing nontrivial pseudocharacters on a free group F n invariant with respect to certain types of endomorphisms. We find some conditions for endomorphisms of the free group under which there is a nontrivial pseudocharacter that is invariant with respect to these endomorphisms. We consider free products $ R = \tilde{R}*\prod\limits_{{i = k}}^n {\left\langle {{r_i}} \right\rangle } $ , where one factor is F n , and the other factor is a group on which there is a pseudocharacter. For such products we obtain a similar result about the conditions of existence of nontrivial pseudocharacters invariant with respect to certain endomorphisms.  相似文献   

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For a wide class of Abelian groups, necessary and sufficient conditions under which a group admits an automorphism of order qn are found; we also present necessary and sufficient conditions under which a group admits an automorphism ϕ of order qn such that ϕqm is a fixed-point-free automorphism for some m < n. Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 239–249, February, 1977.  相似文献   

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(Semi-) planar groups of stable planes are introduced, and information about their size and their structure is derived. A special case are the stabilizers of quadrangles in compact connected projective planes (i.e. automorphism groups of locally compact connected ternary fields).  相似文献   

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This paper concerns 4-dimensional (topological locally compact connected) Minkowski planes that admit a 7-dimensional automorphism group . It is shown that such a plane is either classical or has a distinguished point that is fixed by the connected component of and that the derived affine plane at this point is a 4-dimensional translation plane with a 7-dimensional collineation group.This research was supported by a Feodor Lynen Fellowship.  相似文献   

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It is shown that a translation plane of order which admits two homology groups of order must in fact admit symmetric homology groups of this order. It is further shown that a plane admitting such symmetric index 3 homology groups is, with a finite number of exceptions, a generalized André plane. A list of the possibly exceptional orders is determined. Received 20 March 2000.  相似文献   

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