A proof of a conjecture by Jabara on groups in which all involutions are odd transpositions

Author:

Bettio Egle1

Affiliation:

1. Liceo G. B. Benedetti – N. Tommaseo , Castello 2835 – 30122 , Venezia , Italy

Abstract

Abstract In this paper, we prove that if 𝐺 is a group generated by elements of order two with the property that the product of any two such elements has order 1, 2, 3 or 5 with all possibilities occurring, then G A 5 G\simeq A_{5} or G PSU ( 3 , 4 ) G\simeq\mathrm{PSU}(3,4) . This provides an affirmative answer to Problem 19.36 in the Kourovka notebook.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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1. Groups in which all involutions are 3-transvections;Monatshefte für Mathematik;2024-01-25

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