1. Let G and H be groups, and let g € G and h & H. Find a formula for the order ofthe element (g, h) = G × H in terms of the order of g in G and the order of h in H.

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Answered: 1. Let G and H be groups, and let g E G…

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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Assignment: Q1: Let G be and acG 8.t a finite group la1=12.If H= (a> find all other generalors of H.
Let G be a group and a € G be such that o(r) = 20. Find the orders of a, at, 10, r14 and 30
.google.com/forms/d/e/1FAlpQLSdVIM7rUaPq7ausjooo7qJ5MERrfowHddglBpPLV -Hgq4QQ/for 110 Choose the correct answer If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 and 30 then the order of G is: * О з0 O 60 O 80 О 90
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he following is a multiplication table for a group G. The product a * b is given in the ble where a is from the leftmost column and b from the top row. Let H e V W X Y 2 = e e V W X W V Y Z X W X Y e W X Z V SOSN e What are the orders of the elements? X 3 Y 2 Y 2 Z X V Y e e X W V W e V Y 3 NS Y ১৯৯ {e, z). Show that this is a subgroup of G. Calculate the right cosets of H. Without calculating the left cosets of H, explain why H is a normal subgroup of G. Construct a multiplication table for the quotient group G/H. Is G/H cyclic? Give reasons. Describe the subgroup Z ≤ G/H generated by the element Hx = G/H. What is the order of (G/H)/Z?
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1. Let G and H be groups, and let g E G and he H. Find a formula for the order of the element (g, h) E G x H in terms of the order of g in G and the order of h in H.