1 results
ON MALLE’S CONJECTURE FOR THE PRODUCT OF SYMMETRIC AND NILPOTENT GROUPS
- Part of
-
- Journal:
- Nagoya Mathematical Journal , First View
- Published online by Cambridge University Press:
- 17 February 2025, pp. 1-26
-
- Article
- Export citation
-
Let G be a finite nilpotent group and
$n\in \{3,4, 5\}$. Consider 
$S_n\times G$ as a subgroup of 
$S_n\times S_{|G|}\subset S_{n|G|}$, where G embeds into the second factor of 
$S_n\times S_{|G|}$ via the regular representation. Over any number field k, we prove the strong form of Malle’s conjecture (cf. Malle (2002, Journal of Number Theory 92, 315–329)) for 
$S_n\times G$ viewed as a subgroup of 
$S_{n|G|}$. Our result requires that G satisfies some mild conditions.
