QUESTION 7Suppose thatp: G Gis a group homomorphism. Show that$(e) = (e)(i) For every gEG, (gN-=0(g).(iii) Kero is a normal subgroup of G.%3DAttach FileBrowse Local FilesQUESTION 8be an integral domain and define a relationDXD such that b0 and d0 by (a,b) ~(c,d)if andLetnסonly ifProve that the relation is an equivalence relation.ad%3bcAttach FileBrowse Local Files QUESTION 1Show that the set (5,10,25, 35) is a group under multiplication modulo 40 by constructing its Cayley table. What isthe identity element in the group?Attach FileBrowse Local FilesQUESTION 2Is the group in question 1 cyclic? Substantiate,Attach FileBrowse Local Files

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QUESTION 1 Show that the set 5,10,25, 35} is a group under multiplication modulo 40 by constructing its Cayley table. Wha the identity element in the group? Attach File Browse Local Files

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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