# Descendant subgroup

From Encyclopedia of Mathematics

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2010 Mathematics Subject Classification: *Primary:* 20F14 [MSN][ZBL]

A subgroup of a group for which there is a descending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its predecessor. The series may be an infinite subgroup system. If the series is finite, then the subgroup is subnormal.

## References

- Martyn R. Dixon, "Sylow Theory, Formations, and Fitting Classes", in
*Locally Finite Groups*(World Scientific, 1994) ISBN 9810217951, p.6

**How to Cite This Entry:**

Descendant subgroup.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Descendant_subgroup&oldid=31032