Injectors of finite solvable groups |
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| Authors: | Zvi Arad David Chihag |
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| Affiliation: | 1. Department of Mathematics , University of Chcago , Chicago, ILL, 60637, U.S.ACurrent Address;2. Bar Han University Ramat Gan , Israel;3. Department of Mathematics , Technion, I.I.T , Haifa, Israel |
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| Abstract: | It is well known that in a free group the simple commutator [Y, X](alternatively called the first Engel word) can be expressed as a product of squares. Likewise the second Engel word [Y, X, X] can be expressed as a product of cubes. Results on groups of exponent four imply that the fifth Engel word [Y, X, X, X, X, X] can be expressed as a product of fourth powers, and explicit expressions have now been obtained with the assistance of a computer. The results and the computeraided technique are described. |
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