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It is proved that each of compact linear groups of one special type admits apolynomial factorization map onto a real vector space. More exactly, the groupis supposed to be non-commutative one-dimensional and to have two connectedcomponents, and its representation should be the direct sum of threeirreducible two-dimensional real representations at least two of them beingfaithful.

The existence of a polynomial factorization map for some compact linear groups