Finite groups with some restriction on the vanishing set
| Autor: | Sesuai Yash Madanha, Bernardo Gabriel Rodrigues |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Finite group
Pure mathematics Algebra and Number Theory 20C15 010102 general mathematics Group Theory (math.GR) 010103 numerical & computational mathematics 01 natural sciences Set (abstract data type) Mathematics::Logic Mathematics::Group Theory Solvable group FOS: Mathematics Order (group theory) Computer Science::Symbolic Computation 0101 mathematics Element (category theory) Mathematics - Group Theory Mathematics |
| Zdroj: | Communications in Algebra. 48:5474-5481 |
| ISSN: | 1532-4125 0092-7872 |
| Popis: | Let $ x $ be an element of a finite group $ G $ and denote the order of $ x $ by $ \mathrm{ord}(x) $. We consider a finite group $ G $ such that $ \gcd(\mathrm{ord}(x),\mathrm{ord}(y))\leqslant 2 $ for any two vanishing elements $ x $ and $ y $ contained in distinct conjugacy classes. We show that such a group $ G $ is solvable. When $ G $ with the property above is supersolvable, we show that $ G $ has a normal metabelian $ 2 $-complement. Comment: 9 pages |
| Databáze: | OpenAIRE |
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