## Abstract

Let V denote a vector space over two-element field F_{2} with finite positive dimension and endowed with a symplectic form B. Let SL(V) denote the special linear group of V. Let S denote a subset of V. Define Tv(S) as the subgroup of SL(V) generated by the transvections with direction α for all α∈S. Define G(S) as the graph whose vertex set is S and where α, β∈S are connected whenever B(α, β)=1. A well-known theorem states that under the assumption that S spans V, the following (i) and (ii) are equivalent: (i) Tv(S) is isomorphic to a symmetric group;(ii) G(S) is a claw-free block graph. We give an example which shows that this theorem is not true. We also give a modification of this theorem as follows. Assume that S is a linearly independent set of V and no element of S is in the radical of V. Then (i) and (ii) are equivalent.

Original language | English |
---|---|

Pages (from-to) | 437-442 |

Number of pages | 6 |

Journal | Quarterly Journal of Mathematics |

Volume | 64 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2013 |