Question
Let G = ⟨g⟩ be a cyclic group of order n = 480 = 253151, H be a subgroup of G, and m is the smallest natural number for which gm ∈ H. For which natural numbers m a) the index|G:H|ofGpoH sedelin2; b) the row|H|ofH sedelina2; c) the index|G:H|of G by H sedelina2 and sedelina3; d) the row|H|ofH sedline2 and isedline3.
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Answer to a math question Let G = ⟨g⟩ be a cyclic group of order n = 480 = 253151, H be a subgroup of G, and m is the smallest natural number for which gm ∈ H. For which natural numbers m a) the index|G:H|ofGpoH sedelin2; b) the row|H|ofH sedelina2; c) the index|G:H|of G by H sedelina2 and sedelina3; d) the row|H|ofH sedline2 and isedline3.
Maude
4.7107 Answers
a) To find the possible values of m m |H| |H| m
Answer:m = 16, 32, 64
b) For condition (b), we need to findm |H| |H| m
Answer:m = 1, 2, 4, 8, 15, 30, 60
c) To satisfy condition (c), we look form |H| |H| m
Answer:m = 6, 16
d) For condition (d), we need to findm |H| |H| m
Answer:m = 1, 2, 4, 5, 10, 20
Answer:
b) For condition (b), we need to find
Answer:
c) To satisfy condition (c), we look for
Answer:
d) For condition (d), we need to find
Answer:
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