Finite groups with 2-closed or 2′-closed centralizers of involutions

Finite nonsolvable groups are described whose involution centralizers are 2-closed or 2-closed, whereas the Sylow p-subgroups for p>2 are cyclic.Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 437–446, October, 1971.In conclusion, the author expresses his gratitude to A. I. Starostin for posing the problem and for scientific guidance.