@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},
}