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6. The group of symmetries of the tetrahedron has the following permutations: e= (1)(2)3(4); r, = (1)(234); p, = (1)(243); r, = (2{143); P; = (2)(134); r, = (3)(124); P, = (3)(142); = (4)(132); p. = (4(123); o, = (14)(23); o, = (24)(13); o, = (34)(12); Show that H = {e, r, Pa) is a subgroup of this group by showing closure under composition. Find all the right cosets gH, of H.

6. The group of symmetries of the tetrahedron has the following permutations: e= (1)(2)3(4); r, = (1)(234); p, = (1)(243); r, = (2{143); P; = (2)(134); r, = (3)(124); P, = (3)(142); = (4)(132); p. = (4(123); o, = (14)(23); o, = (24)(13); o, = (34)(12); Show that H = {e, r, Pa) is a subgroup of this group by showing closure under composition. Find all the right cosets gH, of H.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. The group of symmetries of the tetrahedron has the following permutations: e = (1)(2)3(4); r, = (1)(234); P, = (1)(243); r, = (2{143); P; = (2)(134); r, = (3)(124); p, = (3)(142); = (4)(132); p. = (4(123); o, = (14)(23); o, = (24)(13); a, = (34)(12); Show that H = {e, r,, Pa) is a subgroup of this group by showing closure under composition. Find all the right cosets gH, of H.
Transcribed Image Text:6. The group of symmetries of the tetrahedron has the following permutations: e = (1)(2)3(4); r, = (1)(234); P, = (1)(243); r, = (2{143); P; = (2)(134); r, = (3)(124); p, = (3)(142); = (4)(132); p. = (4(123); o, = (14)(23); o, = (24)(13); a, = (34)(12); Show that H = {e, r,, Pa) is a subgroup of this group by showing closure under composition. Find all the right cosets gH, of H.
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