A group G is said to be a PC-group, if G/CG (Xg) is a polycyclic-by-finite group for all xEG. A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.
Russo, F., Trabelsi, N. (2009). On minimal non-PC-groups. ANNALES MATHÉMATIQUES BLAISE PASCAL, 16(2), 277-286 [10.5802/ambp.267].
On minimal non-PC-groups
RUSSO, Francesco;
2009-01-01
Abstract
A group G is said to be a PC-group, if G/CG (Xg) is a polycyclic-by-finite group for all xEG. A minimal non-PC-group is a group which is not a PC-group but all of whose proper subgroups are PC-groups. Our main result is that a minimal non-PC-group having a non-trivial finite factor group is a finite cyclic extension of a divisible abelian group of finite rank.
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