Splitting via Noncommutativity

Mark Lanning Lewis, Daria Lytkina, Viktor Danilovich Mazurov, Ali Reza Moghaddamfar

Результат исследования: Научные публикации в периодических изданияхстатья


Let G be a nonabelian group and n a natural number. We say that G has a strict n-split decomposition if it can be partitioned as the disjoint union of an abelian subgroup A and n nonempty subsets B-1, B-2, . . . , B-n, such that vertical bar B-i vertical bar > 1 for each i and within each set B-i, no two distinct elements commute. We show that every finite nonabelian group has a strict n-split decomposition for some n. We classify all finite groups G, up to isomorphism, which have a strict n-split decomposition for n = 1, 2, 3. Finally, we show that for a nonabelian group G having a strict n-split decomposition, the index vertical bar G : A vertical bar is bounded by some function of n.

Язык оригиналаанглийский
Страницы (с-по)1051-1082
Число страниц32
ЖурналTaiwanese Journal of Mathematics
Номер выпуска5
СостояниеОпубликовано - 1 окт 2018