Some conditions which almost characterize Frobenius groups |
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Authors: | A R Camina |
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Institution: | (1) School of Mathematics and Physics, University of East Anglia, Norwich, England |
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Abstract: | The main result of this paper is the following: LetG be a group with a proper non-trivial normal subgroupH such that each coset ofH distinct fromH is contained in a conjugacy class ofG. IfG is not a Frobenius group with kernelH then one ofH orG/H is ap-group. The hypothesis of this theorem is shown to be equivalent to a condition on characters ofG. The only group the author knows which satisfies this hypothesis and is not either Frobenius or ap-group is one of order 72. |
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