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Identifieur interne : 000400 ( Istex/Curation ); précédent : 000399; suivant : 000401N
Auteurs : V. D. Belousov ; V. E. Plisko ; E. B. Yanovskaya ; D. D. Sokolov ; S. Yu. Maslov ; A. A. Bukhshtab ; V. I. Nechaev ; V. M. Paskonov ; V. A. Artamonov ; A. V. Prokhorov ; N. V. Efimov ; B. V. Khvedelidze ; I. V. Dolgachev ; V. A. Iskovskikh ; A. B. Ivanov ; V. T. Bazylev ; A. V. Arkhangel Ki ; A. A. Sapozhenko ; P. S. Saltan ; P. S. Soltan ; V. A. Chuyanov ; M. Sh. Farber ; S. V. Shvedenko ; V. P. Petrenko ; I. P. Mysovskikh ; V. A. Trenogin ; M. K. Samarin ; Yu. A. Kuznetsov ; E. D. Solomentsev ; M. S. Nikulin ; L. D. Kudryavtsev ; V. N. Latyshev ; D. V. Anosov ; A. L. Shmel In ; L. N. Shevrin ; L. V. Kuz In ; V. L. Popov ; D. V. Alekseevski ; V. N. Remeslennikov ; P. L. Dobrushin ; V. V. Prelov ; G. S. Khovanski ; A. L. Onishchik ; A. K. Tolpygo ; L. A. Sidorov ; L. A. Bokut ; A. Ya. Kiruta ; E. A. Palyutin ; A. D. Ta Manov ; E. I. Vilkas ; V. V. Rumyantsev ; E. G. D Akonov ; A. F. Shapkin ; L. E. Evtushik ; V. I. Sobolev ; V. M. Starszhinski ; S. J. Pokhozhaev ; V. G. Karmanov ; M. I. Voitsekhovski ; Yu. V. Komlenko ; Ya. Yu. Nikitin ; V. N. Grishin ; V. A. Sadovnichi ; Yu. I. Rudyak ; A. G. Dragalin ; E. A. Gorin ; O. A. Ivanova ; V. I. Danilov ; N. M. Nagorny ; D. N. Akhiezer ; R. A. Minlos ; A. D. Bryuno ; V. M. Millionshchikov ; S. A. Stepanov ; N. N. Vil Ams ; P. S. Aleksandrov ; A. A. Talalyan ; G. L. Litvinov ; N. I. Klimov ; A. A. Karatsuba ; I. P. Kubilyus ; N. Kh. RozovSource :
- Encyclopaedia of Mathematics ; 1995.
Abstract
Abstract: A generalization of the concept of a group to the case of an n-ary operation. An n-group is a universal algebra with one n-ary associative operation that is uniquely invertible at each place (cf. Algebraic operation). The theory of n-groups for n⩾3 substantially differs from the theory of groups (i.e. 2-groups). Thus, if n⩾3, an n-group has no analogue of the unit element.
Url:
DOI: 10.1007/978-1-4899-3791-9_2
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Shvedenko</name></author><author><name sortKey="Petrenko, V P" sort="Petrenko, V P" uniqKey="Petrenko V" first="V. P." last="Petrenko">V. P. Petrenko</name></author><author><name sortKey="Mysovskikh, I P" sort="Mysovskikh, I P" uniqKey="Mysovskikh I" first="I. P." last="Mysovskikh">I. P. Mysovskikh</name></author><author><name sortKey="Trenogin, V A" sort="Trenogin, V A" uniqKey="Trenogin V" first="V. A." last="Trenogin">V. A. Trenogin</name></author><author><name sortKey="Samarin, M K" sort="Samarin, M K" uniqKey="Samarin M" first="M. K." last="Samarin">M. K. Samarin</name></author><author><name sortKey="Kuznetsov, Yu A" sort="Kuznetsov, Yu A" uniqKey="Kuznetsov Y" first="Yu. A." last="Kuznetsov">Yu. A. Kuznetsov</name></author><author><name sortKey="Solomentsev, E D" sort="Solomentsev, E D" uniqKey="Solomentsev E" first="E. D." last="Solomentsev">E. D. Solomentsev</name></author><author><name sortKey="Nikulin, M S" sort="Nikulin, M S" uniqKey="Nikulin M" first="M. S." last="Nikulin">M. S. Nikulin</name></author><author><name sortKey="Kudryavtsev, L D" sort="Kudryavtsev, L D" uniqKey="Kudryavtsev L" first="L. D." last="Kudryavtsev">L. D. Kudryavtsev</name></author><author><name sortKey="Latyshev, V N" sort="Latyshev, V N" uniqKey="Latyshev V" first="V. N." last="Latyshev">V. N. Latyshev</name></author><author><name sortKey="Anosov, D V" sort="Anosov, D V" uniqKey="Anosov D" first="D. V." last="Anosov">D. V. Anosov</name></author><author><name sortKey="Shmel In, A L" sort="Shmel In, A L" uniqKey="Shmel In A" first="A. L." last="Shmel In">A. L. Shmel In</name></author><author><name sortKey="Shevrin, L N" sort="Shevrin, L N" uniqKey="Shevrin L" first="L. N." last="Shevrin">L. N. Shevrin</name></author><author><name sortKey="Kuz In, L V" sort="Kuz In, L V" uniqKey="Kuz In L" first="L. V." last="Kuz In">L. V. Kuz In</name></author><author><name sortKey="Popov, V L" sort="Popov, V L" uniqKey="Popov V" first="V. L." last="Popov">V. L. Popov</name></author><author><name sortKey="Alekseevski, D V" sort="Alekseevski, D V" uniqKey="Alekseevski D" first="D. V." last="Alekseevski">D. V. Alekseevski</name></author><author><name sortKey="Remeslennikov, V N" sort="Remeslennikov, V N" uniqKey="Remeslennikov V" first="V. N." last="Remeslennikov">V. N. Remeslennikov</name></author><author><name sortKey="Dobrushin, P L" sort="Dobrushin, P L" uniqKey="Dobrushin P" first="P. L." last="Dobrushin">P. L. Dobrushin</name></author><author><name sortKey="Prelov, V V" sort="Prelov, V V" uniqKey="Prelov V" first="V. V." last="Prelov">V. V. Prelov</name></author><author><name sortKey="Khovanski, G S" sort="Khovanski, G S" uniqKey="Khovanski G" first="G. S." last="Khovanski">G. S. Khovanski</name></author><author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name></author><author><name sortKey="Tolpygo, A K" sort="Tolpygo, A K" uniqKey="Tolpygo A" first="A. K." last="Tolpygo">A. K. Tolpygo</name></author><author><name sortKey="Sidorov, L A" sort="Sidorov, L A" uniqKey="Sidorov L" first="L. A." last="Sidorov">L. A. Sidorov</name></author><author><name sortKey="Bokut, L A" sort="Bokut, L A" uniqKey="Bokut L" first="L. A." last="Bokut">L. A. Bokut</name></author><author><name sortKey="Kiruta, A Ya" sort="Kiruta, A Ya" uniqKey="Kiruta A" first="A. Ya." last="Kiruta">A. Ya. Kiruta</name></author><author><name sortKey="Palyutin, E A" sort="Palyutin, E A" uniqKey="Palyutin E" first="E. A." last="Palyutin">E. A. Palyutin</name></author><author><name sortKey="Ta Manov, A D" sort="Ta Manov, A D" uniqKey="Ta Manov A" first="A. D." last="Ta Manov">A. D. Ta Manov</name></author><author><name sortKey="Vilkas, E I" sort="Vilkas, E I" uniqKey="Vilkas E" first="E. I." last="Vilkas">E. I. Vilkas</name></author><author><name sortKey="Rumyantsev, V V" sort="Rumyantsev, V V" uniqKey="Rumyantsev V" first="V. V." last="Rumyantsev">V. V. 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G. Karmanov</name></author><author><name sortKey="Voitsekhovski, M I" sort="Voitsekhovski, M I" uniqKey="Voitsekhovski M" first="M. I." last="Voitsekhovski">M. I. Voitsekhovski</name></author><author><name sortKey="Komlenko, Yu V" sort="Komlenko, Yu V" uniqKey="Komlenko Y" first="Yu. V." last="Komlenko">Yu. V. Komlenko</name></author><author><name sortKey="Nikitin, Ya Yu" sort="Nikitin, Ya Yu" uniqKey="Nikitin Y" first="Ya. Yu." last="Nikitin">Ya. Yu. Nikitin</name></author><author><name sortKey="Grishin, V N" sort="Grishin, V N" uniqKey="Grishin V" first="V. N." last="Grishin">V. N. Grishin</name></author><author><name sortKey="Sadovnichi, V A" sort="Sadovnichi, V A" uniqKey="Sadovnichi V" first="V. A." last="Sadovnichi">V. A. Sadovnichi</name></author><author><name sortKey="Rudyak, Yu I" sort="Rudyak, Yu I" uniqKey="Rudyak Y" first="Yu. I." last="Rudyak">Yu. I. Rudyak</name></author><author><name sortKey="Dragalin, A G" sort="Dragalin, A G" uniqKey="Dragalin A" first="A. G." last="Dragalin">A. G. Dragalin</name></author><author><name sortKey="Gorin, E A" sort="Gorin, E A" uniqKey="Gorin E" first="E. A." last="Gorin">E. A. Gorin</name></author><author><name sortKey="Ivanova, O A" sort="Ivanova, O A" uniqKey="Ivanova O" first="O. A." last="Ivanova">O. A. Ivanova</name></author><author><name sortKey="Danilov, V I" sort="Danilov, V I" uniqKey="Danilov V" first="V. I." last="Danilov">V. I. Danilov</name></author><author><name sortKey="Nagorny, N M" sort="Nagorny, N M" uniqKey="Nagorny N" first="N. M." last="Nagorny">N. M. Nagorny</name></author><author><name sortKey="Akhiezer, D N" sort="Akhiezer, D N" uniqKey="Akhiezer D" first="D. N." last="Akhiezer">D. N. Akhiezer</name></author><author><name sortKey="Minlos, R A" sort="Minlos, R A" uniqKey="Minlos R" first="R. A." last="Minlos">R. A. Minlos</name></author><author><name sortKey="Bryuno, A D" sort="Bryuno, A D" uniqKey="Bryuno A" first="A. D." last="Bryuno">A. D. Bryuno</name></author><author><name sortKey="Millionshchikov, V M" sort="Millionshchikov, V M" uniqKey="Millionshchikov V" first="V. M." last="Millionshchikov">V. M. Millionshchikov</name></author><author><name sortKey="Stepanov, S A" sort="Stepanov, S A" uniqKey="Stepanov S" first="S. A." last="Stepanov">S. A. Stepanov</name></author><author><name sortKey="Vil Ams, N N" sort="Vil Ams, N N" uniqKey="Vil Ams N" first="N. N." last="Vil Ams">N. N. Vil Ams</name></author><author><name sortKey="Aleksandrov, P S" sort="Aleksandrov, P S" uniqKey="Aleksandrov P" first="P. S." last="Aleksandrov">P. S. Aleksandrov</name></author><author><name sortKey="Talalyan, A A" sort="Talalyan, A A" uniqKey="Talalyan A" first="A. A." last="Talalyan">A. A. Talalyan</name></author><author><name sortKey="Litvinov, G L" sort="Litvinov, G L" uniqKey="Litvinov G" first="G. L." last="Litvinov">G. L. Litvinov</name></author><author><name sortKey="Klimov, N I" sort="Klimov, N I" uniqKey="Klimov N" first="N. I." last="Klimov">N. I. Klimov</name></author><author><name sortKey="Karatsuba, A A" sort="Karatsuba, A A" uniqKey="Karatsuba A" first="A. A." last="Karatsuba">A. A. Karatsuba</name></author><author><name sortKey="Kubilyus, I P" sort="Kubilyus, I P" uniqKey="Kubilyus I" first="I. P." last="Kubilyus">I. P. Kubilyus</name></author><author><name sortKey="Rozov, N Kh" sort="Rozov, N Kh" uniqKey="Rozov N" first="N. Kh." last="Rozov">N. Kh. Rozov</name></author></analytic><monogr></monogr><series><title level="s">Encyclopaedia of Mathematics</title><imprint><date>1995</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: A generalization of the concept of a group to the case of an n-ary operation. An n-group is a universal algebra with one n-ary associative operation that is uniquely invertible at each place (cf. Algebraic operation). The theory of n-groups for n⩾3 substantially differs from the theory of groups (i.e. 2-groups). Thus, if n⩾3, an n-group has no analogue of the unit element.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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