Anti-CC-groups and anti-PC-groups. (Q925484)

Summary: A group \(G\) has Chernikov classes of conjugate subgroups if the quotient group \(G/\text{core}_G(N_G(H))\) is a Chernikov group for each subgroup \(H\) of \(G\). An anti-CC group \(G\) is a group in which each nonfinitely generated subgroup \(K\) has the quotient group \(G/\text{core}_G(N_G(K))\) a Chernikov group. Analogously, a group \(G\) has polycyclic-by-finite classes of conjugate subgroups if the quotient group \(G/\text{core}_G(N_G(H))\) is a polycyclic-by-finite group for each subgroup \(H\) of \(G\). An anti-PC group \(G\) is a group in which each nonfinitely generated subgroup \(K\) has the quotient group \(G/\text{core}_G(N_G(K))\) a polycyclic-by-finite group. Anti-CC groups and anti-PC groups are the subject of the present article.