Geodesic
CLASSIFICATION OF FINITE GROUPS VIA THEIR BREADTH
Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 544-563

Voir la notice de l'article provenant de la source Cambridge University Press

Let k be a divisor of a finite group G and Lk(G) = {x ∈ G | xk =1}. Frobenius proved that the number |Lk(G)| is always divisible by k. The following inverse problem is considered: for a given integer n, find all groups G such that max{k-1|Lk(G)| | k ∈ Div(G)} = n, where Div(G) denotes the set of all divisors of |G|. A procedure beginning with (in a sense) minimal members and deducing the remaining ones is outlined and executed for n=8. 
HEINEKEN, HERMANN; RUSSO, FRANCESCO G. CLASSIFICATION OF FINITE GROUPS VIA THEIR BREADTH. Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 544-563. doi: 10.1017/S0017089519000272
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     title = {CLASSIFICATION {OF} {FINITE} {GROUPS} {VIA} {THEIR} {BREADTH}},
     journal = {Glasgow mathematical journal},
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