Solvable linear groups over division rings

Solvable linear groups over division rings
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 91 (1984), 341-344

DOI: https://doi.org/10.1090/S0002-9939-1984-0744625-3

PDF | Request permission

A solvable subgroup of ${\text {G}}{{\text {L}}_n}\left ( D \right )$ whose linear span is ${M_n}\left ( D \right )$ is abelian-by-locally finite.

References

A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Research Notes in Mathematics, vol. 44, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980. MR 590045
Edward Formanek and Arun Vinayak Jategaonkar, Subrings of Noetherian rings, Proc. Amer. Math. Soc. 46 (1974), 181–186. MR 414625, DOI 10.1090/S0002-9939-1974-0414625-5
B. Hartley and M. A. Shahabi Shojaei, Finite groups of matrices over division rings, Math. Proc. Cambridge Philos. Soc. 92 (1982), no. 1, 55–64. MR 662960, DOI 10.1017/S0305004100059697
Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601
A. I. Lichtman, On embedding of group rings in division rings, Israel J. Math. 23 (1976), no. 3-4, 288–297. MR 432692, DOI 10.1007/BF02761806
Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211

Finiteness conditions and generalized soluble groups

Robert L. Snider, The zero divisor conjecture for some solvable groups, Pacific J. Math. 90 (1980), no. 1, 191–196. MR 599330
B. A. F. Wehrfritz, Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76, Springer-Verlag, New York-Heidelberg, 1973. MR 0335656
B. A. F. Wehrfritz, Nilpotence in certain linear groups over division rings, Proc. London Math. Soc. (3) 46 (1983), no. 2, 334–346. MR 693044, DOI 10.1112/plms/s3-46.2.334
B. A. F. Wehrfritz, The upper central factors of certain skew-linear groups, Arch. Math. (Basel) 40 (1983), no. 6, 481–494. MR 710013, DOI 10.1007/BF01192815
A. E. Zalesskiĭ, The structure of certain classes of matrix groups over a sfield, Sibirsk. Mat. Ž. 8 (1967), 1284–1298 (Russian). MR 0220843