On a factorization of an iterated wreath product of permutation groups

Beata Bajorska, Vitaliy Sushchansky

Abstract


We show that if each group of permutations \((G_i, M_i),\ i\in\mathbb{N}\) has a factorization then their infinite iterated wreath product \(\mathop{\hbox{\(\wr\)}}\limits_{i=1}^{\infty}\!\! G_i\) also has a factorization. We discuss some properties of this factorization and give examples.


Keywords


iterated wreath product of permutation groups, factorization of groups, profinite groups

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