A Generalization of Neumann’s Question
| Autor: | Mohammad Zarrin, Soran Marzang, N. Ahmadkhah |
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| Rok vydání: | 2018 |
| Předmět: |
Generalization
Group (mathematics) Applied Mathematics 010102 general mathematics 0102 computer and information sciences 01 natural sciences Combinatorics Mathematics (miscellaneous) Cardinality 010201 computation theory & mathematics Bounded function 0101 mathematics Commutative property Mathematics |
| Zdroj: | Results in Mathematics. 73 |
| ISSN: | 1420-9012 1422-6383 |
| DOI: | 10.1007/s00025-018-0844-3 |
| Popis: | Let G be a group, $$m\ge 2$$ and $$n\ge 1$$ . We say that G is an $$\mathcal {T}(m,n)$$ -group if for every m subsets $$X_1, X_2, \dots , X_m$$ of G of cardinality n, there exists $$i\ne j$$ and $$x_i \in X_i, x_j \in X_j$$ such that $$x_ix_j=x_jx_i$$ . In this paper, we give some examples of finite and infinite non-Abelian $$\mathcal {T}(m,n)$$ -groups and we discuss finiteness and commutativity of such groups. We also show solvability length of a solvable $$\mathcal {T}(m,n)$$ -group is bounded in terms of m and n. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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