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- W4362700448 abstract "Abstract We introduce the abstract concept of supernilpotence in loop theory, and relate it to existing concepts, namely, central nilpotence and nilpotence of the multiplication group. We prove that the class of supernilpotence is greater or equal than the class of nilpotence of the multiplication group, and combining existing results, we show that a finite loop is supernilpotent if and only if its multiplication group is nilpotent. We also provide a new exposition of a classical result and crucial ingredient, that loops with a nilpotent multiplication group are centrally nilpotent and admit a prime decomposition." @default.
- W4362700448 created "2023-04-09" @default.
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- W4362700448 date "2023-04-07" @default.
- W4362700448 modified "2023-09-26" @default.
- W4362700448 title "Three Concepts of Nilpotence in Loops" @default.
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- W4362700448 doi "https://doi.org/10.1007/s00025-023-01882-x" @default.
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