Permutative APS

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This term is related to: APS theory
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Definition

A permutative APS of groups is an APS of groups (G,\Phi) equipped with an APS-on-APS action on it by the permutation IAPS, having the following property:

If \sigma: \{ 1,2,3,\dots,m+n \} \to \{ 1,2,3,\dots,m+n \} is a permutation defined as:

\sigma(j) = n + j, \qquad 1 \le j \le m

and:

\sigma(j) = j - m, \qquad m + 1 \le j \le n

Then, for g \in G_m, h \in G_n, we have:

\Phi_{n,m}(h,g) = \sigma \cdot \Phi_{m,n}(g,h)