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1.
We show that in the constructible universe, the two usual definitions of Butler groups are equivalent for groups of arbitrarily
large power. We also prove that Bext2(G, T) vanishes for every torsion-free groupG and torsion groupT. Furthermore, balanced subgroups of completely decomposable groups are Butler groups. These results have been known, under
CH, only for groups of cardinalities ≤ ℵω.
Partial support by NSF is gratefully acknowledged.
Partially supported by U.S.-Israel Binational Science Foundation. 相似文献
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Loyiso G. Nongxa 《manuscripta mathematica》1999,100(2):159-171
A necessary and sufficient condition is derived for an arbitrary cyclic regulating almost completely decomposable group to
belong to a K(n)-class, n≥ 0. This allows one to formulate a Structure Theorem for clipped p-primary cyclic regulating groups in each K(n)-class. Using the Indecomposability Criterion we construct an example of an indecomposable balanced Butler group which does
not have a unique regulating subgroup.
Received: 3 November 1998 相似文献
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Under various set-theoretic hypotheses we construct families of maximal possible size of almost free abelian groups which
are pairwise almost disjoint, i.e. there is no non-free subgroup embeddable in two of them. We show that quotient-equivalent
groups cannot be almost disjoint, but we show how to construct maximal size families of quotient-equivalent groups of cardinality
ℵ1, which are mutually non-embeddable.
Dedicated to the memory of Abraham Robinson on the tenth anniversary of this death
First and third authors acknowledge assistance from the US-Israel Binational Science Foundation, Grant No. 1110. First author
partially supported by NSF Grant No. MCS-8003691. Second author acknowledges support from the National Science and Engineering
Research Council of Canada, Grant No. U0075 相似文献
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It is well known [BF] that in the constructible universe (V=L) the class ofB
1-groups is closed under prebalanced subgroups. A similar attempt at the increasing countable unions of prebalanced subgroups
has been done in [B]. Here we give an affirmative answer to a similar question concerning the so-calledP B
∞-subgroups.
This research was initiated while the first author was on a short visit at the University of Colorado, Colorado Springs, in
February 1994 and supported by Charles University grant GAUK 45/94. 相似文献
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Fuchs and Rangaswamy [8] proved that a smooth ascending union G = U α<λ Gα of pure B2-subgroups is a B2-group provided either λ = ωo or λ = ω1,/G/ = N1 and all the subgroups Gα are decent in G. In this paper, we extend this result to arbitrary cardinal numbers λ under suitable hypotheses on the factor-groups G α+1/G α. 相似文献
11.
Fred Galvin 《Proceedings of the American Mathematical Society》1996,124(6):1723-1725
A permutation group on a set of (infinite) cardinality is almost disjoint if no element of except the identity has fixed points, i.e., if is an almost disjoint family of subsets of . We show how almost disjoint permutation groups can be constructed from almost disjoint families of sets.
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Witold Jarczyk 《Aequationes Mathematicae》2010,80(1-2):141-154
The notion of almost convexity is studied and an extension of Kuczma’s theorem, originally proved in finite-dimensional spaces, is presented. The phrase “almost” is meant in the sense of abstract σ-ideals. The main result also generalizes the theorem proved in Jarczyk and Laczkovich (Math Inequal Appl 13:217–225, 2009). 相似文献
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B.A.F. Wehrfritz 《Journal of Pure and Applied Algebra》2011,215(5):1112-1115
Suppose G is either a soluble (torsion-free)-by-finite group of finite rank or a soluble linear group over a finite extension field of the rational numbers. We consider the implications for G if G has an automorphism of finite order m with only finitely many fixed points. For example, if m is prime then G is a finite extension of a nilpotent group and if m=4 then G is a finite extension of a centre-by-metabelian group. This extends the special cases where G is polycyclic, proved recently by Endimioni (2010); see [3]. 相似文献
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E. A. Blagoveshchenskaya 《Journal of Mathematical Sciences》2008,152(2):137-154
Realization and classification theorems are obtained for a class of commutative rings with identities and almost completely
decomposable additive structures. A necessary and sufficient condition for the considered rings to have isomorphic additive
structures is also found.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 3–27, 2006. 相似文献
18.
E. M. Kovyazina 《Mathematical Notes》1996,60(6):666-670
It is proved that a τ-adic relation characterizing a Butler group is piecewise rational.
Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 882–887, December, 1996. 相似文献
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IfM is a closed Nil geometry 3-manifold then 1(M) is almost convex with respect to a fairly simple geometric generating set. IfG is a central extension or a extension of a word hyperbolic group, thenG is also almost convex with respect to some generating set. Combining these with previously known results shows that ifM is a closed 3-manifold with one of Thurston's eight geometries, 1(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol. 相似文献