Splitting via Noncommutativity
| Autor: | Lewis, M. L., Lytkina, D. V., Mazurov, V. D., Moghaddamfar, A. R. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Taiwanese Journal of Mathematics, 2018 |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $B_1, B_2, \ldots, B_n$, such that $|B_i| > 1$ 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 $|G:A|$ is bounded by some function of $n$. Comment: 31 pages |
| Databáze: | arXiv |
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