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- Group_of_symplectic_type abstract "In mathematical finite group theory, a p-group of symplectic type is a p-group such that all characteristic abelian subgroups are cyclic. According to Thompson (1968, p.386), the p-groups of symplectic type were classified by P. Hall in unpublished lecture notes, who showed that they are all a central product of an extraspecial group with a group that is cyclic, dihedral, quasidihedral, or quaternion. Gorenstein (1980, 5.4.9) gives a proof of this result.The width n of a group G of symplectic type is the largest integer n such that the group contains an extraspecial subgroup H of order p1+2n such that G = H.CG(H), or 0 if G contains no such subgroup. Groups of symplectic type appear in centralizers of involutions of groups of GF(2)-type.".
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- Group_of_symplectic_type wikiPageRevisionID "541662924".
- Group_of_symplectic_type hasPhotoCollection Group_of_symplectic_type.
- Group_of_symplectic_type subject Category:Finite_groups.
- Group_of_symplectic_type type Abstraction100002137.
- Group_of_symplectic_type type FiniteGroups.
- Group_of_symplectic_type type Group100031264.
- Group_of_symplectic_type comment "In mathematical finite group theory, a p-group of symplectic type is a p-group such that all characteristic abelian subgroups are cyclic. According to Thompson (1968, p.386), the p-groups of symplectic type were classified by P. Hall in unpublished lecture notes, who showed that they are all a central product of an extraspecial group with a group that is cyclic, dihedral, quasidihedral, or quaternion.".
- Group_of_symplectic_type label "Group of symplectic type".
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