TY - JOUR
ID - 2674
TI - Covering monolithic groups with proper subgroups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Garonzi, Martino
AD - University of Padova
Y1 - 2013
PY - 2013
VL - 2
IS - 1
SP - 131
EP - 144
KW - Covers
KW - Monolithic groups
KW - Primitive groups
DO - 10.22108/ijgt.2013.2674
N2 - Given a finite non-cyclic group $G$, call $\sigma(G)$ the smallest number of proper subgroups of $G$ needed to cover $G$. Lucchini and Detomi conjectured that if a nonabelian group $G$ is such that $\sigma(G) < \sigma(G/N)$ for every non-trivial normal subgroup $N$ of $G$ then $G$ is monolithic, meaning that it admits a unique minimal normal subgroup. In this paper we show how this conjecture can be attacked by the direct study of monolithic groups.
UR - https://ijgt.ui.ac.ir/article_2674.html
L1 - https://ijgt.ui.ac.ir/article_2674_ea33a8a83df38a9fbe3ccb5bf483e473.pdf
ER -