Loop geometries

We introduce the construction of the semidirect product of a loop and its associate (or quasigroup)-the group uniquely generated by the loop. For a (left or right) loop the semidirect product is a group acting transitively on the loop so that the loop is provided with the structure of a homogeneous space, the stationary subgroup being its associate. The construction is reversible, viz. any homogeneous space can be provided with the structure of a loop so that the semidirect product of it with the transassociate is isomorphic with the fundamental group of the homogeneous space and the transassociate is isomorphic with the stationarity group. © 1973 Consultants Bureau.

Авторы
Журнал
Номер выпуска
5
Язык
Английский
Страницы
799-805
Статус
Опубликовано
Том
12
Год
1972
Организации
  • 1 Patrice Lumumba University, Russia
Цитировать
Поделиться

Другие записи

Prostakov N.S., Govor S.Ya., Mikheeva N.N., Karlos R., Franko P.
Химия гетероциклических соединений. Латвийский институт органического синтеза Латвийской академии наук / Springer New York Consultants Bureau. Том 5. 1972. С. 764-766