Order has only two prime factors implies prime divisor with larger class two subgroups is core-nontrivial
From Groupprops
Statement
Suppose and are two distinct primes, and is a group of order for nonnegative integers . Suppose denotes the maximum of the orders of -subgroups of of nilpotence class two. Then, if , is a core-nontrivial prime divisor of : has a normal -subgroup.
Related facts
- Order has only two prime factors implies solvable
- order has only two prime factors implies prime divisor with larger prime power is core-nontrivial except in finitely many cases
References
Journal references
- On Burnside's other p^aq^b-theorem by George Glauberman, Pacific Journal of Mathematics, Volume 56, Page 469 - 476(Year 1975): This paper proves that Order has only two prime factors implies prime divisor with larger class two subgroups is core-nontrivial.^{Project Euclid page}^{More info}