___

• S. Bachmuth, Automorphisms of free metabelian groups, Trans. Amer. Math. Soc.,118 (1965), 93-104.
• R. H. Fox, Free differential calculus I-Derivation in the free group ring, Ann. Math., 57 (1953), 547-560.
• C. K. Gupta and E. I. Timoshenko, Generation elements for groups of the form F/R0, Algebra Logika, 40(3) (2001), 251-261.
• C. K. Gupta and W. Holubowski, On 2-symmetry words in nilpotent groups, Ukrainian Math. J., 54(7) (2002), 1227-1233.
• W. Holubowski, Symmetric words in metabelian groups, Comm. Algebra, 23 (1995), 5161-5167.
• W. Holubowski, Note on symmetric words in metabelian groups, Ukrainian Math. J., 54 (2002), 1218-1220.
• O. Macedo´nska and D. Solitar, On binary σ-invariant words in a group, Con- temp. Math., 97 (1994), 431-449.
• W. Magnus, On a theorem of Marshall Hall, Ann. Math., 40 (1939), 764-768.
• J. M. Pan, On 2-symmetric words and verbal subgroup of metabelian product of abelian groups, Algebra Colloq., 13(3) (2006), 535-540.
• E. Plonka, Symmetric words in nilpotent groups of class ≤ 3, Fund. Math., 97 (1977), 95-103.
• N. S. Romanovskii, Shmel’kin embedding for abstract and profinite groups, Algebra Logika, 38(5) (1999), 598-612.
• A. L. Shmel’kin, Some factor groups in free products. Proc. I. G. Petroskiis Seminar, 5 (1979), 209-216.
• W. Tomaszewski, Automorphisms permuting generators in groups and their fixed points, Ph. D. Thesis, Silesian University, Katowice 1999. Jiangmin Pan
• Department of Mathematics School of Mathematics and Statistics Yunnan University Kunming 650031 P. R. China e-mail: jmpan@ynu.edu.cn