Author:
Hickman J.L.,Neumann B.H.
Abstract
László Babai raised the question whether every infinite group G contains a set B of elements, of cardinal equal to the order of G, such that for elements a, b, c of B the equation a = bc−1b implies a = c. We show that the answer is affirmative for certain classes of groups, including the soluble groups and the countable groups, if the Axiom of Choice is assumed, but negative, even for abelian groups, if a different axiom, compatible with Zermelo-Fraenkel set theory but incompatible with the Axiom of Choice, is assumed.
Publisher
Cambridge University Press (CUP)
Reference6 articles.
1. [2] Babai László , in litt.
2. Small sets with large power sets
3. Periodic Groups of Odd Exponent
4. [5] Monro G.P. , “Some independence results for weak axioms of choice” (PhD thesis, University of Bristol, 1971).
Cited by
4 articles.
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