Difference between revisions of "T-group"
From Encyclopedia of Mathematics
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| − | * Derek Robinson, "A Course in the Theory of Groups", Graduate Texts in Mathematics '''80''' Springer (1996) ISBN 0-387-94461-3 | + | * Derek Robinson, "A Course in the Theory of Groups", Graduate Texts in Mathematics '''80''' Springer (1996) {{ISBN|0-387-94461-3}} {{ZBL|0483.20001}} |
Latest revision as of 20:32, 18 November 2023
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
How to Cite This Entry:
T-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=T-group&oldid=51479
T-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=T-group&oldid=51479