Speaker: Bui Xuan Hai (University of Natural Sciences, Hochiminh City)
Time: 9h00, 16/4/2014
Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract:: Let D be a division ring with center F, and D* be the multiplicative group of D. The existence of non-cyclic free subgroups in D* has been posed as a conjecture by Lichtman when he studied the analogue of Tits' Alternative for matrix rings over division rings. In this talk, we replace D* by any subnormal subgroup G (resp. by any maximal subgroup M) of D*, and then we investigate the same problem for such a G (resp. M). Also, we talk about some conjectures on the existence of free algebras and free group algebras in D.
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