Geodesic
Actions of nilpotent groups on nilpotent groups
Glasgow mathematical journal, Tome 67 (2025) no. 2, pp. 228-231

Voir la notice de l'article provenant de la source Cambridge

DOI

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 $H^1(J,N)$ for abelian $N$. We then show that if $N \rtimes J$ acts on some non-empty set $\Omega$, where the action of $N$ is transitive and for each prime $p$ a Sylow $p$-subgroup of $J$ fixes an element of $\Omega$, then $J$ fixes an element of $\Omega$.
DOI : 10.1017/S0017089524000363
Mots-clés : nilpotent-by-nilpotent group actions, primary decompositions in cohomology, fixed points of non-coprime actions 
Burkhart, Michael C. Actions of nilpotent groups on nilpotent groups. Glasgow mathematical journal, Tome 67 (2025) no. 2, pp. 228-231. doi: 10.1017/S0017089524000363
@article{10_1017_S0017089524000363,
     author = {Burkhart, Michael C.},
     title = {Actions of nilpotent groups on nilpotent groups},
     journal = {Glasgow mathematical journal},
     pages = {228--231},
     year = {2025},
     volume = {67},
     number = {2},
     doi = {10.1017/S0017089524000363},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000363/}
}
TY  - JOUR
AU  - Burkhart, Michael C.
TI  - Actions of nilpotent groups on nilpotent groups
JO  - Glasgow mathematical journal
PY  - 2025
SP  - 228
EP  - 231
VL  - 67
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000363/
DO  - 10.1017/S0017089524000363
ID  - 10_1017_S0017089524000363
ER  - 
%0 Journal Article
%A Burkhart, Michael C.
%T Actions of nilpotent groups on nilpotent groups
%J Glasgow mathematical journal
%D 2025
%P 228-231
%V 67
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000363/
%R 10.1017/S0017089524000363
%F 10_1017_S0017089524000363

Cité par Sources :