Assume that N is a normal subgroup of a group G. Assume E is asubgroup of G/N. As in Problem 10.3.11 , let K be the union of all thecosets in E. Show that K is normal in G if and only if E is normal inG/N.
Assume that N is a normal subgroup of a group G. Assume E is asubgroup of G/N. As in Problem 10.3.11 , let K be the union of all thecosets in E. Show that K is normal in G if and only if E is normal inG/N.
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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Assume that N is a normal subgroup of a group G. Assume E is a
subgroup of G/N. As in Problem 10.3.11 , let K be the union of all the
cosets in E. Show that K is normal in G if and only if E is normal in
G/N.
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