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Let n and k be positive integers. We consider the (ordinary) depth of several Young subgroups of the symmetric group Sn. For k<n, Sn−k has depth 2⌊(n−2)/k⌋+1 in Sn. Moreover, for n⩾2k, we show that the depth of S{k+1,…,n}×S{1,…,k}≅Sn−k×Sk in Sn is2⌈2(n−1)k+1⌉−1 in case n⩾(k2+2)/2, and it is 2⌈log2k⌉+1 if n=2k. For 2k<n<(k2+2)/2, we give upper and lower bounds for the depth. Furthermore, we...
This paper continues Fritzsche (2012) [4], where the ordinary depths of the subgroups of G:=PSL(2,q) with q a prime power are determined. Now, we will pay attention to the minimal combinatorial depths of the subgroups of G. It turns out that most of the subgroups have a minimal combinatorial depth ⩽7, and often it coincides with the ordinary depth of this subgroup in G. However, if H⩽G is of order...
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