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References
C. Baginski, Groups of units of modular group algebras. Proc. Amer. Math. Soc.101, 619–624 (1987).
A. K. Bhandari andI. B. S. Passi, Residually Lie nilpotent group rings. Arch. Math.58, 1–6 (1992).
A. K.Bhandari and I. B. S.Passi, Lie nilpotency indices of group algebras. To appear in Bull. London Math. Soc.
D. B.Coleman, Private communication. 1990.
D. B. Coleman andD. S. Passman, Units in modular group rings. Proc. Amer. Math. Soc.25, 510–512 (1970).
X. Du, The centres of a radical ring. Canad. Math. Bull.35, 174–179 (1992).
N. D. Gupta andF. Levin, On the Lie ideals of a ring. J. Algebra81, 225–231 (1983).
S. A. Jennings, The structure of the group ring of ap-group over a modular field. Trans. Amer. Math. Soc.50, 175–185 (1941).
S. A. Jennings, Radical rings with nilpotent associated groups. Trans. Roy. Soc. Canada (3)49, 31–38 (1955).
S. Koshitani, On the nilpotency indices of the radicals of group algebras ofp-groups which have cyclic subgroups of indexp. Tsukuba J. Math.1, 137–148 (1977).
H. Laue, On the associated Lie ring and the adjoint group of a radical ring. Canad. Math. Buil.27, 215–222 (1984).
A. Lubotzky andA. Mann, Powerfulp-groups. I. Finite groups. J. Algebra105, 484–505 (1987).
A. Mann andA. Shalev, The nilpotency class of the unit group of a modular group algebra II. Israel J. Math.70, 267–277 (1990).
I. B. S.Passi, Group Rings and their Augmentation Ideals. LNM715, Berlin-Heidelberg-New York 1979.
I. B. S. Passi, D. S. Passman andS. K. Sehgal, Lie solvable group rings. Canad. J. Math.25, 748–757 (1973).
I. B. S. Passi andS. K. Sehgal, Lie dimension subgroups. Comm. Algebra3, 59–73, (1975).
D. M. Riley, Restricted Lie dimension subgroups. Comm. Algebra13, 1493–1499 (1991).
A.Shalev, Applications of dimension and Lie dimension subgroups to modular group algebras. Proceedings of the Amitsur Conference in Ring Theory 1989, 84–95. Jerusalem 1989.
A. Shalev, The nilpotency class of the unit group of a modular group algebra I. Israel J. Math.70, 257–266 (1990).
A.Shalev, On some conjectures concerning units inp-group algebras. Proceedings of the 2nd Bressanone Conference in Group Theory 1989, 279–288. Palermo 1990.
A. Shalev, Dimension subgroups, nilpotency indices, and the number of generators of ideals inp-group algebras. J. Algebra129, 412–438 (1990).
A. Shalev, Lie dimension subgroups, Lie nilpotency indices, and the exponent of the group of normalized units. J. London Math. Soc.43, 23–36 (1991).
A. Shalev, Large wreath products in modular group rings. Bull. London Math. Soc.23, 46–52 (1991).
R. K.Sharma and V.Bist, A note on Lie nilpotent group rings. To appear in Bull. Austral. Math. Soc.
R. K. Sharma andJ. B. Srivastava, Lie ideals in group rings. J. Pure Appl. Algebra63, 67–80 (1990).
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Shalev, A. The nilpotency class of the unit group of a modular group algebra III. Arch. Math 60, 136–145 (1993). https://doi.org/10.1007/BF01199099
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DOI: https://doi.org/10.1007/BF01199099