Two collection formulas | Научно-инновационный портал СФУ

Two collection formulas

Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.1515/jgth-2019-0074

Аннотация: Let G be a group, x, y is an element of G, and H is a normal closure in G of the subgroup generated by all commutators of x, y that include more than two occurrences of y. Our main result is a parametrization of the uncollected part of Hall's collection formula for (xy)(n) and two different collection formulas modulo H in an explicit form. In particular, we found explicit expressions for the exponents of the commutators in Hall's collection formula for both known cases and some unknown cases. Also we give combinatorial identities, which simplify those expressions and help to investigate their divisibility. Let G be a group, x, y ∈ G and H is a normal closure in G of the subgroup generated by all commutators of x, y x,y that include more than two occurrences of y. Our main result is a parametrization of the uncollected part of Hall's collection formula for (x y)n and two different collection formulas modulo H in an explicit form. In particular, we found explicit expressions for the exponents of the commutators in Hall's collection formula for both known cases and some unknown cases. Also we give combinatorial identities, which simplify those expressions and help to investigate their divisibility. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.

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Издание

Журнал: JOURNAL OF GROUP THEORY

Выпуск журнала: Vol. 23, Is. 4

Номера страниц: 607-628

ISSN журнала: 14335883

Место издания: BERLIN

Издатель: WALTER DE GRUYTER GMBH

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