Mathematics

Mathematics, 13.07.2019 18:10, aquinomelodyr

Let t = (1,3, 4, 6) (2,3,5) in se. find the index of (t) in se. la che a group of order 21. show that every proper subgroup of g is cyclic.

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Mathematics, 30.06.2019 01:10, kahnerp6448

1. give an example of a group, g, and a proper subgroup, h, where h has finite index in g and h has infinite order 2. give an example of a group, g, and a proper subgroup, h, where h has infinite index in g and h has finite order. (hint: you won't be able to find this with the groups that we work a lot with. try looking in so2(r))

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Mathematics, 13.07.2019 05:20, kkmoney87

If g is a group, then a subgroup h is called characteristic if whenever ø : g -> g is an automorphism, ø(h) = h. prove that a characteristic subgroup is a normal subgroup. the opposite is not true in general. give an example of a group and a proper characteristic subgroup (hint: think about cyclic groups, or the center of a group)

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Mathematics, 18.07.2019 02:30, dothework

1. give an example of a group, g, and a proper subgroup, h, where h has finite index in g and h has infinite order 2. give an example of a group, g, and a proper subgroup, h, where h has infinite index in g and h has finite order. (hint: you won't be able to find this with the groups that we work a lot with. try looking in so2(r))

Answers: 2

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Mathematics, 30.07.2019 18:20, emileewhitaker1373

A. show that {a : 15a ≡ 18 (mod 24)} is not a subgroup of the group z24 (with operation +) b. let g = zm (the operation is addition) and let b be some number with 1 ≤ b < m. show that the cyclic subgroup h generated by b is all of g if and only if the least common multiple of b and m is bm, if and only if (b, m) = 1. c. show that the subgroup of z consisting of all solutions x in z of ax ≡ 0 (mod m) is the cyclic subgroup rz where r = m/(a, m).

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Let t = (1,3, 4, 6) (2,3,5) in se. find the index of (t) in se. la che a group of order 21. show tha...

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