Search results for "P-grupo finito"

p-grupos finitos

1997

In the first part, new bounds for the number of conjugacy classes of maximal length of a finite $p$-group $G$, $r(G)$, are obtained, and they are related with the length of these classes. If $r(G)=p^m-b-1$, there exists a unique normal subgroup of order $p^b$, $N_b$, which is characteristic, and structural properties of these groups are studied when $b\le 3$, by paying special attention to the relation between $N_b$, $Z(G)$ and $G$. In the second part, new bounds for the degree of commutativity of a $p$-group of maximal class are established. In Chapter 2, the bounds known for $c$ are reviewed. In Chapter 3, the reuslts obtained by Shepherd for $c_0\le 4$ are extended to $c_0\le 10$ by mean…