FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 2, PAGES 121-131

**Finite solvable groups in which the Sylow
$p$-subgroups are either bicyclic or of order
$p3$**

V. S. Monakhov

A. A. Trofimuk

Abstract

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All groups considered in this paper will be finite.
Our main result here is the following theorem.
Let $G$ be
a solvable group in which the Sylow $p$-subgroups are either
bicyclic or of order $p3$ for any
$p$Î
p (G).
Then the derived length of $G$ is at
most $6$.
In particular, if $G$ is an $A$_{4}-free group,
then the following statements are true: (1) $G$ is a dispersive
group; (2) if no prime $q$Î p
(G) divides $p2+p+1$ for any
prime $p$Î p
(G), then $G$ is Ore dispersive;
(3) the derived length of $G$ is at
most $4$.

Location: http://mech.math.msu.su/~fpm/eng/k09/k092/k09205h.htm

Last modified: December 22, 2009