Geodesic
The Hughes subgroup
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 4, pp. 283-288

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let \( G \) be a group and \( p \) a prime. The subgroup generated by the elements of order different from \( p \) is called the Hughes subgroup for exponent \( p \). Hughes [3] made the following conjecture: if \( H_{p}(G) \) is non-trivial, its index in \( G \) is at most \( p \). There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case \( p = 3 \) and \( G \) arbitrary, and that of Hogan and Kappe [2] concerning the case when \( G \) is metabelian, and \( p \) arbitrary. A common proof is given for the two cases and a possible lacuna in the first is filled. 
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     title = {The {Hughes} subgroup},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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     publisher = {mathdoc},
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     mrnumber = {MR1320579},
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Bryce, Robert. The Hughes subgroup. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 4, pp. 283-288. http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_4_a0/