Open AccessSome Sufficient conditions for a group to be abelian
Author(s) -
Gary L. Walls
Publication year - 2019
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1901-6
Subject(s) - mathematics , abelian group , group (periodic table) , pure mathematics , word (group theory) , elementary abelian group , g module , algebra over a field , geometry , physics , quantum mechanics
A group is said to satisfy a word $w$ in the symbols $\{x, x^{-1}, y, y^{-1} \}$ provided that if the 'x' and 'y' are replaced by arbitrary elements of the group then the equation $w=1$ is satisfied. This paper studies certain equations in words, as above, which together with other conditions imply that groups which satisfy these equations and conditions must be abelian.
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