Geodesic
Primitive elements of free groups of rank~3
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 445-454

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The automorphism group of the free metabelian group $M_3$ is investigated. It is shown that $M_3$ has primitive elements not induced by primitive elements of $F_3$. A criterion is provided for elements of $M_3$ to be primitive. 
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     author = {V. A. Roman'kov},
     title = {Primitive elements of free groups of rank~3},
     journal = {Sbornik. Mathematics},
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     volume = {73},
     number = {2},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_73_2_a7/}
}
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V. A. Roman'kov. Primitive elements of free groups of rank~3. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 445-454. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a7/