Desolation Island (Aubrey & Maturin, Book 5) by Patrick O'Brian

By Patrick O'Brian

Commissioned to rescue Governor Bligh of Bounty status, Captain Jack Aubrey and his buddy and health care provider Stephen Maturin sail the Leopard to Australia with a carry packed with convicts. between them is a gorgeous and hazardous spy—and a treacherous sickness that decimates the team. With a Dutch man-of-war to windward, the undermanned, outgunned Leopard sails for her existence into the freezing waters of the Antarctic, the place, in mountain seas, the Dutchman closes...

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Extra info for Desolation Island (Aubrey & Maturin, Book 5)

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5). — . Soit A un monoïde (resp. un groupe). L’intersection ⋂i∈I Bi d’une famille (Bi )i∈I de sous-monoïdes de A (resp. de sous-groupes de A) est un sous-monoïde de A (resp. un sous-groupe de A). 3. 6). — Soit A un monoïde (resp. un groupe) et soit S une partie de A. Il existe un plus petit sous-monoïde de A (resp. un plus petit-sous groupe de A) qui contient S. C’est l’intersection de la famille des sous-monoïdes (resp. des sous-groupes) de A qui contiennent S ; on l’appelle le sous-monoïde (resp.

D’après le i = x in = 1, donc l’ordre de a i divise pm i . Comme i = x i i ≠ 1, l’ordre de a i est égal à pm i . Comme les ordres de a i sont premiers entre eux deux à deux, leur produit i a = ∏ a i est d’ordre ∏ pm i = n. Cela prouve que A est cyclique. 7). — Lorsque K est un corps commutatif fini, cette preuve se prête bien à un calcul effectif d’un générateur du groupe multiplicatif K× . Pour déterminer l’élément x i , il suffit d’essayer les éléments un par un. 8. — Soit A un groupe abélien dont la loi de groupe est notée additivement.

De groupes) a) L’image f (A) est un sous-monoïde (resp. un sous-groupe) de B. b) Soit B′ un sous-monoïde (resp. un sous-groupe) de B ; l’image réciproque f −1 (B′ ) est un sous-monoïde (resp. un sous-groupe) de A. c) Soit g ∶ A → B un second morphisme de monoïdes (resp. de groupes). L’ensemble Ker( f , g) des a ∈ A tels que f (a) = g(a) est un sous-monoïde (resp. un sous-groupe) de A. Démonstration. — a) On a eB = f (eA ) ∈ f (A). Soit a, b ∈ f (A) et soit x, y ∈ A tels que a = f (x) et b = f (y) ; alors, ab = f (x) f (y) = f (x y) ∈ f (A).

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