Geodesic
Group extensions and automorphism group rings
Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 53-70.

Voir la notice de l'article provenant de la source International Press of Boston

We use extensions to study the semi-simple quotient of the group ring $\mathbf{F}_pAut(P)$ of a finite $p$-group $P$. For an extension $E: N \to P \to Q$, our results involve relations between $Aut(N)$, $Aut(P)$, $Aut(Q)$ and the extension class $[E]\in H^2(Q, ZN)$. One novel feature is the use of the intersection orbit group $\Omega([E])$, defined as the intersection of the orbits $Aut(N)\cdot[E]$ and $Aut(Q)\cdot [E]$ in $H^2(Q,ZN)$. This group is useful in computing $|Aut(P)|$. In case $N$, $Q$ are elementary Abelian $2$-groups our results involve the theory of quadratic forms and the Arf invariant.
DOI : 10.4310/HHA.2003.v5.n1.a3
Classification : 20J06, 55P42
Keywords: automorphism group, extension class, semi-simple quotient, stable splittings 
@article{HHA_2003_5_1_a2,
     author = {John Martino and Stewart Priddy},
     title = {Group extensions and automorphism group rings},
     journal = {Homology, homotopy, and applications},
     pages = {53--70},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2003},
     doi = {10.4310/HHA.2003.v5.n1.a3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a3/}
}
TY  - JOUR
AU  - John Martino
AU  - Stewart Priddy
TI  - Group extensions and automorphism group rings
JO  - Homology, homotopy, and applications
PY  - 2003
SP  - 53
EP  - 70
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a3/
DO  - 10.4310/HHA.2003.v5.n1.a3
LA  - en
ID  - HHA_2003_5_1_a2
ER  - 
%0 Journal Article
%A John Martino
%A Stewart Priddy
%T Group extensions and automorphism group rings
%J Homology, homotopy, and applications
%D 2003
%P 53-70
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a3/
%R 10.4310/HHA.2003.v5.n1.a3
%G en
%F HHA_2003_5_1_a2
John Martino; Stewart Priddy. Group extensions and automorphism group rings. Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 53-70. doi : 10.4310/HHA.2003.v5.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a3/

Cité par Sources :