Let [Formula: see text], [Formula: see text] or [Formula: see text], act freely on a finitistic connected space [Formula: see text]. This paper gives the cohomology classification of [Formula: see text] if the mod 2 or rational cohomology of the orbit space [Formula: see text] is isomorphic to the product of a projective space and sphere [Formula: see text], where [Formula: see text] or [Formula: see text], respectively. For a free involution on [Formula: see text], a lower bound of covering dimension of the coincidence set of a continuous map [Formula: see text] is also determined.
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Kumari et al. (2024) studied this question.
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