On some invariants of finite groups

Document Type: Ischia Group Theory 2012

Authors

1 Institute of Mathematics, University of Warsaw

2 Institute of Mathematics University of Białystok

Abstract

A normal subgroup $N$ of a group $G$ is said to be an‎ omissible subgroup of $G$ if it has the following property‎: ‎whenever $X\leq G$ is such that $G=XN$‎, ‎then $G=X$‎. ‎In this note we construct various groups $G$‎, ‎each of which has an omissible subgroup $N\neq 1$ such that $G/N\cong SL_2(k)$ where $k$ is a field of positive characteristic‎.

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