Abstract
We study the functional equation
for all \(x, y, z\in G\), \(f_i: G\rightarrow H, i=1, 2, \ldots , 7\), where G is a group, H is an abelian group, and we present its general solution when G is a free group. Solutions on other selected groups are also given.
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The author is most grateful to the anonymous referee for the careful reading of the manuscript and valuable suggestions.
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This work was partially supported by the National Natural Science Foundation of China (Grant No. 11971081), Foundation of Chongqing Municipal Education Commission (Grant No. KJQN201900525) the Natural Science Foundation of Chongqing (Grant No. cstc2020jcyj-msxmX0857), Research Project of Chongqing Education Commission (Grant No. CXQT21014).
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Luo, Y., Zhao, H.Y. A Pexiderization of Whitehead’s Equation. Results Math 78, 23 (2023). https://doi.org/10.1007/s00025-022-01800-7
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DOI: https://doi.org/10.1007/s00025-022-01800-7