A characterization of finite symplectic polar spaces of odd prime order

Authors:
Binod Kumar Sahoo;N.S. Narasimha Sastry
Affiliations:
Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, R.V. College Post, Bangalore 560059, India;Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, R.V. College Post, Bangalore 560059, India
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

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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 p^1^+^2^r and of exponent p (Theorems 1.5 and 1.6).