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ON THE SETS CVCV IN THE GROUP SL(n, K)

1995
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Demonstratio Mathematica
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In [3] has been proved that (1) if A € SL(n, K) is not a scalar and K has at least four elements, then A is a commutator of SL(n,K). In a present paper we shall prove that (2) if A € SL(n,K) is not a scalar and n < \K\ -1 or char/i = 0, then there exists class CV such that A G CyCy-x, where Cy denotes the conjugacy class of V € SL{n, K). Observe that the condition A 6 CyCy-1 implies that A is a commutator. Hence if n < \K\ -1 or char K = 0, then the second theorem is stronger than the first

doi:10.1515/dema-1995-0318
fatcat:6u7xk2l6avdwphrqk5d5kvfrfu