TY - JOUR

T1 - What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?

AU - Brusyanskaya, Elena K.

AU - Klyachko, Anton A.

AU - Vasil'ev, Andrey V.

N1 - Publisher Copyright: © 2019 Mathematical Sciences Publishers. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/10

Y1 - 2019/10

N2 - Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation xn = 1 in a group, the Solomon theorem (1969) on the number of solutions in a group to a system of equations having fewer equations than unknowns, and the Iwasaki theorem (1985) on roots of subgroups. There are other curious corollaries on groups and rings.

AB - Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation xn = 1 in a group, the Solomon theorem (1969) on the number of solutions in a group to a system of equations having fewer equations than unknowns, and the Iwasaki theorem (1985) on roots of subgroups. There are other curious corollaries on groups and rings.

KW - Equations in groups

KW - Frobenius's theorem

KW - Iwasaki's theorem

KW - Solomon's theorem

KW - VERTICAL-BAR-HOM(A

KW - equations in groups

KW - EQUATIONS

KW - CHARACTERS

UR - http://www.scopus.com/inward/record.url?scp=85077089632&partnerID=8YFLogxK

U2 - 10.2140/pjm.2019.302.437

DO - 10.2140/pjm.2019.302.437

M3 - Article

AN - SCOPUS:85077089632

VL - 302

SP - 437

EP - 452

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -