Maximal subgroup has prime power index in finite solvable group
From Groupprops
Statement
Let be a finite solvable group and
be a maximal subgroup of
. Then, the index
is a power of a prime.
Facts used
References
Textbook references
- Finite Groups by Daniel Gorenstein, ISBN 0821843427, More info, Page 219, Theorem 1.5 (Section 6.1)
- Abstract Algebra by David S. Dummit and Richard M. Foote, 10-digit ISBN 0471433349, 13-digit ISBN 978-0471433347, More info, Page 200, Exercise 32, Section 6.1 (
-groups, nilpotent groups and solvable groups)