Computing Whitehead groups using genetic bases
نویسندگان
چکیده
منابع مشابه
Whitehead Groups of Finite Groups
In 1966, Milnor surveyed in this Bulletin [23] the concept of Whitehead torsion, focusing on the definition, topological significance and computation of Whitehead groups and their relationship to algebraic ^-theory and the congruence subgroup problem. As Milnor showed in that survey [23, Appendix 1], an affirmative solution to the congruence subgroup problem for algebraic number fields would im...
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We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.
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We investigate the Whiteheadness of Borel abelian groups (א1-free, without loss of generality as otherwise this is trivial). We show that CH (and even WCH) implies any such abelian group is free, and always א2-free. 1998 Mathematics Subject Classification 03C60, 03E15, 20K20.
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In this paper we discuss a genetic version (GWA) of the Whitehead’s algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead’s algorithm in free groups of rank ≥ 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead’s Problem ...
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The connections between Whitehead groups and uniformization properties were investigated by the third author in [9]. In particular it was essentially shown there that there is a non-free Whitehead (respectively, א1-coseparable) group of cardinality א1 if and only if there is a ladder system on a stationary subset of ω1 which satisfies 2-uniformization (respectively, ω-uniformization). (See also...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.12.011