By C.; Hemery, C. Lebosse

Manuel scolaire de mathématiques, niveau seconde C, programmes de 1965. Algèbre. Cet ouvrage fait partie de l. a. assortment Lebossé-Hémery dont les manuels furent à l’enseignement des mathématiques ce que le Bled et le Bescherelle furent à celui du français.

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**Extra resources for Algèbre. Classe de Seconde C**

**Example text**

Let 8 G J . Since G

Let N be a regular normal subgroup of the group G on Ω. Let a e Ω. In addition let A be the group of automorphisms which N undergoes under similarity transformations by the elements g e G a , considered as a permutation group on N — 1. Then the permutation groups G a on Ω — OL and A on N — 1 differ only in the designation of points; the "point" n of the second group corresponds to the point ocn of the first. Proof. Let y, δ G Ω — a and let g e G a take γ into δ. In addition let c and d be the corresponding "points" oî N — 1, hence c = (ay ···) ··· and d = (αδ ···) ···.

U < H and (I yH I, I H : U I) = 1 fift^/v y" = r · In what follows let G be transitive on Î2 and let oc e Ω be given. Let the lengths of the orbits of G a , ordered according to increasing magnitude, be 1 = nx < n2 < ··· < nk . 4. If there exists an index j > 1 such that ηό > n2nj_1, then G is imprimitive. Proof. Let Δ be the union of those orbits whose length is