A group $G$ has Chernikov classes of conjugate subgroups if the quotient group $G/ core_G(N_G(H))$ 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 $G/core_G(N_G(K))$ which is a Chernikov group. Analogously, a group $G$ has polycyclic-by-finite classes of conjugate subgroups if the quotient group $G/core_G(N_G(H))$ 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 $G/core_G(N_G(K))$ which is a polycyclic-by-finite group. Anti-$CC$-groups and anti-$PC$-groups are the subject of the present article.

Russo, F. (2007). Anti-$PC$-groups and Anti-$CC$-groups. INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2007 [doi:10.1155/2007/29423].

Anti-$PC$-groups and Anti-$CC$-groups

RUSSO, Francesco
2007-01-01

Abstract

A group $G$ has Chernikov classes of conjugate subgroups if the quotient group $G/ core_G(N_G(H))$ 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 $G/core_G(N_G(K))$ which is a Chernikov group. Analogously, a group $G$ has polycyclic-by-finite classes of conjugate subgroups if the quotient group $G/core_G(N_G(H))$ 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 $G/core_G(N_G(K))$ which is a polycyclic-by-finite group. Anti-$CC$-groups and anti-$PC$-groups are the subject of the present article.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
Russo, F. (2007). Anti-$PC$-groups and Anti-$CC$-groups. INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2007 [doi:10.1155/2007/29423].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/55682
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