On a factorization of an iterated wreath product of permutation groups

• Дата: 2018
• Автори: Bajorska, Beata, Sushchansky, Vitaliy
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: iterated wreath product of permutation groups; factorization of groups; profinite groups; 20E22; 20E18
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1043
• Назва журналу: Algebra and Discrete Mathematics

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.