@article{TEXTUAL, recid = {14670}, author = {Burkhart, Michael C.}, title = {Actions of nilpotent groups on nilpotent groups}, journal = {Glasgow Mathematical Journal}, address = {2025-01-16}, number = {TEXTUAL}, abstract = {For finite nilpotent groups J and N, suppose J acts on N via automorphisms. We exhibit a decomposition of the first cohomology set in terms of the first cohomologies of the Sylow p-subgroups of J that mirrors the primary decomposition of H<sup>1</sup>(J, N) for abelian N. We then show that if N ⋊ J acts on some non-empty set Ω, where the action of N is transitive and for each prime p a Sylowp-subgroup of J fixes an element of Ω, then J fixes an element of Ω.}, url = {http://knowledge.uchicago.edu/record/14670}, }