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Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split quaternions and two real nonlinear systems, we derive explicit formulas for computing the roots of x 2 + b x + c = 0 in split quaternion algebra. [ABSTRACT FROM AUTHOR]

Let {Gr,i} be a sequence of r-generator subgroups of U(1,n; ℂ) and Gr be its algebraic limit group. In this paper, two algebraic convergence theorems concerning {Gr,i} and Gr are obtained. Our results are generalisations of their counterparts in the n-dimensional sense-preserving Möbius group. [ABSTRACT FROM PUBLISHER]

In this paper we show that the answer to problem 3.9 in [Duke Math. J. 69 (1993) 593] is positive when n=2 and negative when n⩾3. [Copyright &y& Elsevier]