Abstract
Letk be any finite or infinite cardinal andS ω the symmetric group of denumerable infinite degree. It is shown that fori<k ifG i is thei-th row of a matrix whose columns are allk-termed sequences of elements ofS ω in each of which all but a finite number of terms are equal to the identity ofS ω thenG i 's (withG −1 i 's defined in an obvious way and with coordinatewise multiplication amongG i 's andG i −1's) generate the Free Group onk free generatorsG i . Analogously, Free Abelian and other types of free groups are also constructed.
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Abian, A. A new construction of free groups. Algebra Universalis 10, 130–132 (1980). https://doi.org/10.1007/BF02482896
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DOI: https://doi.org/10.1007/BF02482896