let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow‎ ‎$2$-subgroup of $g$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎by $n_g(p)$ we denote the normalizer of‎ ‎$p$ in $g$‎. ‎in this paper‎, ‎we show that $n_g(p)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

This study examined the probability of (a) being placed in a disciplinary alternative education setting for mandatory versus discretionary reasons and (b) returning within the same year among an ethnically diverse sample (African American, Caucasian, Hispanic) of middle and high school students (N=270). Participants were compared based on ethnicity, gender, grade level, and special education st...

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson summation formulas for these sequences. Moreover, give some identities matrices related with Furthermore, show that there are close relations between p-Leonardo-Lucas, numbers Fibonacc...