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Two collection formulas

  • Sergey Kolesnikov , Vladimir Leontiev and Georgy Egorychev
From the journal Journal of Group Theory


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 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.

Communicated by Nigel Boston


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Received: 2019-05-23
Revised: 2020-01-30
Published Online: 2020-03-19
Published in Print: 2020-07-01

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