we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.

Abstract Many financial instruments are designed with embedded leverage, such as options and leveraged exchange-traded funds (ETFs). Embedded leverage alleviates investors’ constraints, and, therefore, we hypothesize that lowers required returns. Consistent this hypothesis, find empirically ETFs provide significant amounts of leverage; increases return volatility in proportion to the higher is ...