Words and Almost Nilpotent Varieties of Groups # |
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Authors: | Qianlu Li |
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Institution: | 1. Institute of Mathematics , University of Mons-Hainaut, “Le Pentagone” , Mons, Belgium;2. Mons, Belgium and Department of Mathematics , YanBei Teacher's College , DaTong Shanxi, China li@umh.ac.be |
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Abstract: | For a word of a free group of rank n , the author obtains an invariant called its standard exponent, and shows that if any residually finite group satisfying the law defined by such a word is almost nilpotent, then the standard exponent of the word equals 1 . Conversely, if the standard exponent of a word ω is 1 , then any residually finite or soluble group and any locally finite or soluble group satisfying the group law ω≡ 1 is nilpotent-of-bounded-class-by-bounded-exponent. |
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Keywords: | Almost nilpotent Standard exponent Variety Word |
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