Abstract
A multiplication on an H-space X has a left inverse λ and a right inverse ρ. They are mutual inverses and λ = ρ if and only if \(\). In this paper we investigate the order \(\) of λ. We give an example of a multiplication with \(\), and prove that for any finite H-complex X there are finitely many left inverses of finite order. Conditions are given for there to be infinitely many multiplications on X with the same left inverse. We then give conditions for a left inverse to have infinite order. We apply these results to specific Lie groups.
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