View source for T-group

{{TEX|done}}{{MSC|20E15}}

A [[group]] $G$ in which normality is transitive: if $N$ is a [[normal subgroup]] of $G$, and $H$ is a normal subgroup of $N$, then $H$ is a normal subgroup of $G$.  Equivalently, every [[subnormal subgroup]] of $G$ is normal in $G$.  Every [[completely reducible group]] is a T-group; the [[dihedral group]] of order 8 is the smallest finite group that is not a T-group.  A group is a T-group if and only if it is equal to its own [[Wielandt subgroup]].


====References====
* Derek Robinson, "A Course in the Theory of Groups", Graduate Texts in Mathematics '''80''' Springer (1996) ISBN 0-387-94461-3  {{ZBL|0483.20001}}