Character expansiveness in finite groups
We say that a finite group $G$ is conjugacy expansive if for anynormal subset $S$ and any conjugacy class $C$ of $G$ the normalset $SC$ consists of at least as many conjugacy classes of $G$ as$S$ does. Halasi, Mar'oti, Sidki, Bezerra have shown that a groupis conjugacy expansive if and only if...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2013-06-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://www.theoryofgroups.ir/?_action=showPDF&article=1660&_ob=4335a14289e50a35e7186085ea9a408c&fileName=full_text.pdf |
| Summary: | We say that a finite group $G$ is conjugacy expansive if for anynormal subset $S$ and any conjugacy class $C$ of $G$ the normalset $SC$ consists of at least as many conjugacy classes of $G$ as$S$ does. Halasi, Mar'oti, Sidki, Bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.By considering a character analogue of the above, we say that afinite group $G$ is character expansive if for any complexcharacter $alpha$ and irreducible character $chi$ of $G$ thecharacter $alpha chi$ has at least as many irreducibleconstituents, counting without multiplicity, as $alpha$ does. Inthis paper we take some initial steps in determining characterexpansive groups. |
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| ISSN: | 2251-7650 2251-7669 |