The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers. Insoluble groups which satisfy the one-prime power hypothesis have been classified. However it has remained an o...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2019-12-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf |
| Summary: | We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers. Insoluble groups which satisfy the one-prime power hypothesis have been classified. However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups. In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups. |
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| ISSN: | 2251-7650 2251-7669 |