A characterization of finite symplectic polar spaces of odd prime order |
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Authors: | Binod Kumar Sahoo NS Narasimha Sastry |
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Institution: | Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, R.V. College Post, Bangalore 560059, India |
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Abstract: | A sufficient condition for the representation group for a nonabelian representation (Definition 1.1) of a finite partial linear space to be a finite p-group is given (Theorem 2.9). We characterize finite symplectic polar spaces of rank r at least two and of odd prime order p as the only finite polar spaces of rank at least two and of prime order admitting nonabelian representations. The representation group of such a polar space is an extraspecial p-group of order p1+2r and of exponent p (Theorems 1.5 and 1.6). |
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Keywords: | Generalized quadrangles Polar spaces Nonabelian representations Extraspecial p-groups |
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