CHARACTERIZATION OF THE GROUPS D<sub>p+1</sub>(2) AND D<sub>p+1</sub>(3) USING ORDER COMPONENTS
CHARACTERIZATION OF THE GROUPS D<sub>p+1</sub>(2) AND D<sub>p+1</sub>(3) USING ORDER COMPONENTS
In this paper we will prove that the groups <TEX>$D_{p+1}$</TEX>(2) and <TEX>$D_{p+1}$</TEX>(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson's conjecture for the groups <TEX>$D_{p+1}$</TEX>(2) and <TEX>$D_{p+1}$</TEX>(3).