Geodesic
Nilpotent by Supersolvable M-Groups
Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 934-962

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

A character of a finite group G is monomial if it is induced from a linear (degree one) character of a subgroup of G. A group G is an M-group if all its complex irreducible characters (the set Irr(G)) are monomial.In [1], Dade gave an example of an M-group with a normal subgroup which is itself not an M-group. In his group G, the supersolvable residual N is an extra special 2-group and G/N is supersolvable of even order. Moreover, the prime 2 is used in such a way that no analogous construction is possible in the case that |N| or |G:N| is odd. This led Isaacs in [8] and Dade in [2] to consider the effect of certain “oddness“ hypotheses in the study of monomial characters.Our main results are in the same spirit. Although our techniques seem to require a restrictive assumption on the supersolvable residual of the groups we consider, our theorems provide more evidence that under fairly general circumstances normal subgroups of M-groups should be M-groups. 
Parks, Alan E. Nilpotent by Supersolvable M-Groups. Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 934-962. doi: 10.4153/CJM-1985-051-0
@article{10_4153_CJM_1985_051_0,
     author = {Parks, Alan E.},
     title = {Nilpotent by {Supersolvable} {M-Groups}},
     journal = {Canadian journal of mathematics},
     pages = {934--962},
     year = {1985},
     volume = {37},
     number = {5},
     doi = {10.4153/CJM-1985-051-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-051-0/}
}
TY  - JOUR
AU  - Parks, Alan E.
TI  - Nilpotent by Supersolvable M-Groups
JO  - Canadian journal of mathematics
PY  - 1985
SP  - 934
EP  - 962
VL  - 37
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-051-0/
DO  - 10.4153/CJM-1985-051-0
ID  - 10_4153_CJM_1985_051_0
ER  - 
%0 Journal Article
%A Parks, Alan E.
%T Nilpotent by Supersolvable M-Groups
%J Canadian journal of mathematics
%D 1985
%P 934-962
%V 37
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-051-0/
%R 10.4153/CJM-1985-051-0
%F 10_4153_CJM_1985_051_0

[1] 1. Dade, E. C., Normal subgroups of M-groups need not be M-groups, Math. Z. 133 (1973), 313–317. Google Scholar

[2] 2. Dade, E. C., Monomial characters and normal subgroups, Math. Z. 178 (1981), 401–420. Google Scholar

[3] 3. Gallagher, P. X., Group characters and normal Hall subgroups, Nagoya Math. J. 21 (1962), 223–230. Google Scholar

[4] 4. Hall, M., The theory of groups (Chelsea, New York, 1976). Google Scholar

[5] 5. Hall, P. and Higman, G., On the p-length of p-soluble groups and reduction theorems for Bumside's problem, Proc. London Math. Soc. 6 (1956), 1–42. Google Scholar

[6] 6. Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, 1967). Google Scholar | DOI

[7] 7. Isaacs, I. M., Character theory of finite groups (Academic Press, New York, 1976). Google Scholar

[8] 8. Isaacs, I. M., Primitive characters, normal subgroups, and M-groups, Math. Z. 177 (1981), 267–284. Google Scholar

[9] 9. Seitz, G. M., M-groups and the supersolvable residual, Math. Z. 110 (1969), 101–122. Google Scholar

Cité par Sources :