When studying subgroups of , one often replaces a given subgroup with one of its finite index subgroups so that virtual properties of become actual properties of . In many cases, the finite index subgroup is . For which properties is this a good choice? Our main theorem states that being abelian is such a property. Namely, every virtually abelian subgroup of is abelian.
Michael Handel. Lee Mosher. "Virtually Abelian Subgroups of Are Abelian." Michigan Math. J. 69 (3) 465 - 485, August 2020. https://doi.org/10.1307/mmj/1596700814