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FINITE p-GROUPS WHOSE NON-CENTRAL CYCLIC SUBGROUPS HAVE CYCLIC QUOTIENT GROUPS IN THEIR CENTRALIZERS
In this paper, we classified finite p-groups G such that <TEX>$$C_G(x)/</TEX><TEX>&</TEX><TEX>lt;x</TEX><TEX>&</TEX><TEX>gt;$$</TEX> is cyclic for all non-central elements <TEX>$x{\in}G$</TEX>. This solved a problem proposed By Y. Berkovoch.