Geodesic
Nonuniqueness of semidirect decompositions for~semidirect products with directly decomposable factors and applications for dihedral groups
Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 204-215

Voir la notice de l'article provenant de la source Math-Net.Ru

Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are nontrivial direct products. We deal with a special case of semidirect product when the twisting homomorphism acts diagonally on a direct product, as well as with the case when the extending group is a direct product. We give applications of these results in the case of generalized dihedral groups and classic dihedral groups $D_{2n}$. For $D_{2n}$ we give a complete description of semidirect decompositions and values of minimal permutation degrees.
Keywords: semidirect product, direct product, generalized dihedral group.
Mots-clés : diagonal action 
@article{ADM_2017_23_2_a2,
     author = {Peteris Daugulis},
     title = {Nonuniqueness of semidirect decompositions for~semidirect products with directly decomposable factors and applications for dihedral groups},
     journal = {Algebra and discrete mathematics},
     pages = {204--215},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a2/}
}
TY  - JOUR
AU  - Peteris Daugulis
TI  - Nonuniqueness of semidirect decompositions for~semidirect products with directly decomposable factors and applications for dihedral groups
JO  - Algebra and discrete mathematics
PY  - 2017
SP  - 204
EP  - 215
VL  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a2/
LA  - en
ID  - ADM_2017_23_2_a2
ER  - 
%0 Journal Article
%A Peteris Daugulis
%T Nonuniqueness of semidirect decompositions for~semidirect products with directly decomposable factors and applications for dihedral groups
%J Algebra and discrete mathematics
%D 2017
%P 204-215
%V 23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a2/
%G en
%F ADM_2017_23_2_a2
Peteris Daugulis. Nonuniqueness of semidirect decompositions for~semidirect products with directly decomposable factors and applications for dihedral groups. Algebra and discrete mathematics, Tome 23 (2017) no. 2, pp. 204-215. http://geodesic.mathdoc.fr/item/ADM_2017_23_2_a2/