The New Encyclopędia Britannica: L-ZEncyclopędia Britannica, 1992 - 32 pages |
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Page 275
... subgroup . In many important cases the elements of a group that have certain properties form a subgroup . For example , the one - to - one mappings of the points of the Euclidean plane onto themselves form a group G. Those mappings that ...
... subgroup . In many important cases the elements of a group that have certain properties form a subgroup . For example , the one - to - one mappings of the points of the Euclidean plane onto themselves form a group G. Those mappings that ...
Page 276
... subgroups of order 4 and also 4 subgroups of order 3 . The mapping ( h ) ax'hx from the subgroup H onto the subgroup x'Hx is an isomorphism because products are preserved ( see 178 ) and also inverses are preserved ( 178 ) ( 179 ) ( x ...
... subgroups of order 4 and also 4 subgroups of order 3 . The mapping ( h ) ax'hx from the subgroup H onto the subgroup x'Hx is an isomorphism because products are preserved ( see 178 ) and also inverses are preserved ( 178 ) ( 179 ) ( x ...
Page 277
... subgroup of G , X G2 isomorphic to G , and the ordered pairs ( 1 , x2 ) a subgroup isomorphic to G2 , so that in this natural way G , and G2 may be considered as subgroups of G , X G2 , and because of a simple relation ( see 187 ) the ...
... subgroup of G , X G2 isomorphic to G , and the ordered pairs ( 1 , x2 ) a subgroup isomorphic to G2 , so that in this natural way G , and G2 may be considered as subgroups of G , X G2 , and because of a simple relation ( see 187 ) the ...
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