Sui gruppi finiti i cui sottogruppi non normali hanno tutti lo stesso ordine, II

Zappa, Guido

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 1, pp. 13-21

Résumé

Let $p$ be a prime, $n$ be an integer $\geq 1$ and $G$ be a non Abelian and non Hamiltonian finite $p$-group. $G$ is said to be in $S(p^{n})$ if all non normal subgroups of $G$ have order $p^{n}$. In a previous Note [3] all groups in $S(p^{n})$ ($p$ odd, $n \geq 1$), in $S(2)$, and all groups of exponent $4$ belonging to $S(4)$ were given. In the present Note all groups in $S(2^{n})$ ($n \geq 2$) of exponent $> 4$ are given, and the classification of groups in $S(p^{n})$ for all primes $p$ and all integers $n \geq 1$ is completed.