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Characterizability of the group 2 D p(3) by its order components, where p ≥ 5 is a prime number not of the form 2m + 1

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Abstract

The author will prove that the group 2 D p (3) can be uniquely determined by its order components, where p ≠ 2m + 1 is a prime number, p ≥ 5. More precisely, if OC(G) denotes the set of order components of G, we will prove OC(G) = OC(2 D p (3)) if and only if G is isomorphic to 2 D p (3). A main consequence of our result is the validity of Thompson’s conjecture for the groups under consideration.

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  1. School of Mathematics, College of Science, University of Tehran, Tehran, Iran

    M. R. Darafsheh

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  1. M. R. Darafsheh
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Correspondence to M. R. Darafsheh.

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Darafsheh, M.R. Characterizability of the group 2 D p(3) by its order components, where p ≥ 5 is a prime number not of the form 2m + 1. Acta. Math. Sin.-English Ser. 24, 1117–1126 (2008). https://doi.org/10.1007/s10114-007-6143-7

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  • DOI: https://doi.org/10.1007/s10114-007-6143-7

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