BOUNDING THE ORDERS OF NILPOTENT SUBGROUPS OF SOLVABLE LINEAR GROUPS

Authors：Gao, Yinling^*; Yang, Yong

Source：ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2022, 52(5): 1605-1618.

DOI：10.1216/rmj.2022.52.1605

• nilpotent group
• solvable group
• linear group
• group order

We prove that a nilpotent subgroup H of a finite solvable group G has order at most |V|ss/2 if V is a faithful and completely reducible G-module, where ss = ln(32)/ ln(9). We also find related bounds for nilpotent subgroups of odd order in a solvable linear group. We then further generalize these results to certain chief factors of an arbitrary linear group.