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Answer the followings: 1. Let p = (1 2 4 5) (36) € 56. Find the index of (p) in 56. a. 60 b. 120 C. 180 d. 720 2. Find a subgroup of Z₁2 Z18 that is isomorphic to Z, Z4. A. (4) (6) B. (6) + (9) C. (3) (2) D. (2) (6) Find all abelian groups of order 25. A. Z25, Z5 X Z5 B. Z5, Z5 X Z5 C. Z5, Z5 X Z5, Z5 X Z5 X Z5 D. Z25, Z5 X Z5, Z5 X Z5 X Z5 3.

Answer the followings: 1. Let p = (1 2 4 5) (36) € 56. Find the index of (p) in 56. a. 60 b. 120 C. 180 d. 720 2. Find a subgroup of Z₁2 Z18 that is isomorphic to Z, Z4. A. (4) (6) B. (6) + (9) C. (3) (2) D. (2) (6) Find all abelian groups of order 25. A. Z25, Z5 X Z5 B. Z5, Z5 X Z5 C. Z5, Z5 X Z5, Z5 X Z5 X Z5 D. Z25, Z5 X Z5, Z5 X Z5 X Z5 3.

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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Answer the followings: 1. Let p = (1 2 4 5) (36) € 56. Find the index of (p) in 56. a. 60 b. 120 C. 180 d. 720 2. Find a subgroup of Z₁2 Z18 that is isomorphic to Z, Z4. A. (4) (6) B. (6) + (9) C. (3) (2) D. (2) (6) Find all abelian groups of order 25. A. Z25, Z5 X Z5 B. Z5, Z5 X Z5 C. Z5, Z5 X Z5, Z5 X Z5 X Z5 D. Z25, Z5 X Z5, Z5 X Z5 X Z5 3.
Transcribed Image Text:Answer the followings: 1. Let p = (1 2 4 5) (36) € 56. Find the index of (p) in 56. a. 60 b. 120 C. 180 d. 720 2. Find a subgroup of Z₁2 Z18 that is isomorphic to Z, Z4. A. (4) (6) B. (6) + (9) C. (3) (2) D. (2) (6) Find all abelian groups of order 25. A. Z25, Z5 X Z5 B. Z5, Z5 X Z5 C. Z5, Z5 X Z5, Z5 X Z5 X Z5 D. Z25, Z5 X Z5, Z5 X Z5 X Z5 3.
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