T-group

2020 Mathematics Subject Classification: Primary: 20E15 [MSN][ZBL]

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