By A. Barlotti, P.V. Ceccherini and G. Tallini (Eds.)

**Read Online or Download Combinatorics ’81 in honour of Beniamino Segre, Proceedings of the International Conference on Combinatorial Geometrics and their Applications PDF**

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**Additional info for Combinatorics ’81 in honour of Beniamino Segre, Proceedings of the International Conference on Combinatorial Geometrics and their Applications**

**Example text**

Bartolone The c o e f f i c i e n t k41 o f ( k . ) E K must be n e c e s s a r i l y a f u n c t i o n of kZ1 and 1J Thus from v(x,y)v(O,y) k42: kq1 = f(k21,k42), = f(x,y)+xytf(O,y) 6 f(x,y) = x'+xy+y . 4) +kY +k6 for any ( k . ) E K, where y and 6 are maps s a t i s f y i n g 21 42 +xyBty' = ( x t y ) Y + (xy") + (x+y)xyO. k 21 42 bJ Cons ider a c o l l i n e a t i o n v o f N. J I f v i s i n h e r e n t t o t h e automorphismo o f = c (see l e n a 7), by s e t t i n g E ( C ) = o and ~ ( 0 =) 1 one d e f i n e s a ~ ) t h a t E ( X ) = 1 when x E o f G F ( Z ~i n t o A u ~ G F ( ~such D u { O } (lemma 8 ) .

Boston I 1910, I 1 1918. - - 2. 3. 4. 5. 6. 7. 8. 9. - . BUlow-Str. 16 D 2300 K i e l F. R. Germany Annals of Discrete Mathematics 18 (1983) 37-54 0 North-Holland Publishing Company 37 ON SOME TRANSLATION PLANES ADMITTING A FROBENIUS GROUP OF COLLINEATIONS Claudio Bartolone I n t h i s n o t e we s t a t e some r e s u l t s concerning w i t h t r a n s l a t i o n planes o f dimension 2 over GF(q), where q = p Assume t h a t II r . From now on II w i l l denote such a plane. 2 has a c o l l i n e a t i o n group F o f order q (9-1) s a t i s f y i n g t h e f o l l o w i n g c o n d i t i o n : there e x i s t s a point V E Em such t h a t F f i x e s V und a c t s ( f a i t h f u l l y ) as a Frobenius group on i m - t V j .

7. 8. 9. - . BUlow-Str. 16 D 2300 K i e l F. R. Germany Annals of Discrete Mathematics 18 (1983) 37-54 0 North-Holland Publishing Company 37 ON SOME TRANSLATION PLANES ADMITTING A FROBENIUS GROUP OF COLLINEATIONS Claudio Bartolone I n t h i s n o t e we s t a t e some r e s u l t s concerning w i t h t r a n s l a t i o n planes o f dimension 2 over GF(q), where q = p Assume t h a t II r . From now on II w i l l denote such a plane. 2 has a c o l l i n e a t i o n group F o f order q (9-1) s a t i s f y i n g t h e f o l l o w i n g c o n d i t i o n : there e x i s t s a point V E Em such t h a t F f i x e s V und a c t s ( f a i t h f u l l y ) as a Frobenius group on i m - t V j .