## Moufang Plane

In mathematics, a **Moufang plane**, named for Ruth Moufang, is a type of projective plane, characterised by the property that the group of automorphisms fixing all points of any given line acts transitively on the points not on the line. In other words, symmetries fixing a line allow all the other points to be treated as the same, geometrically. Every Desarguesian plane is a Moufang plane, and (as a consequence of the Artinâ€“Zorn theorem) every finite Moufang plane is Desarguesian, but some infinite Moufang planes are non-Desarguesian planes.

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### Some articles on moufang plane:

**Moufang Plane**

... In mathematics, a

**Moufang plane**, named for Ruth

**Moufang**, is a type of projective

**plane**, characterised by the property that the group of automorphisms fixing all ... Every Desarguesian

**plane**is a

**Moufang plane**, and (as a consequence of the Artinâ€“Zorn theorem) every finite

**Moufang plane**is Desarguesian, but some infinite

**Moufang planes**are non-Desargu ... The projective

**plane**over any alternative division ring is a

**Moufang plane**, and this gives a 11 correspondence between isomorphism classes of alternative division rings and

**Moufang planes**...

### Famous quotes containing the word plane:

“As for the dispute about solitude and society, any comparison is impertinent. It is an idling down on the *plane* at the base of a mountain, instead of climbing steadily to its top.”

—Henry David Thoreau (1817–1862)