On Landau's function g(n)

Jean-Louis Nicolas (1)

1 ICJ - Institut Camille Jordan

Let $S_n$ be the symmetric group of $n$ letters; Landau considered the function $g(n)$ defined as the maximal order of an element of $S_n$. This function is non-decreasing. Let us define the sequence $n_1=1, n_2=2, n_3=3, n_4=4,n_5=5,n_6=7, ...,n_k$ such that $g(n_k) > g(n_k -1)$. It is known that $lim sup n_{k+1}-n_k =infinity$. Here it is shown that $lim inf n_{k+1}-n_k is finite.

Domaines: Théorie des nombres [math.NT]

Jean-Louis Nicolas. On Landau's function g(n). The Mathematics of Paul Erdös I,, 2013, I, pp.207- 220. ⟨10.1007/978-1-4614-7258-2_14⟩. ⟨hal-00916019⟩