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On solvable groups whose Sylow subgroups are either abelian or extraspecial

D. V. Gritsuk, V. S. Monakhov

Francisk Skaryna Gomel State University, Faculty of Mathematics

Abstract: A $p$-group $G$ is called extraspecial if its derived subgroup, center and Frattini subgroup are groups of order $p.$ We consider the solvable groups whose Sylow subgroups are either abelian or extraspecial. It is proved that derived length is at most $2\cdot|\pi(G)|$ and nilpotent length is at most $2+|\pi(G)|$.

UDC: 512.542

Received: 12.11.2012