Let G be a group with operation and H be a group with operation f: G H is a mapping that has properties : V x, y = G, apply f(x * y) = f(x) of (y) f(x-¹) = f(x)-1 show that a) K = {x EG : f(x) = еH} is a subgroup of G eµ} b) R = {f(x) EG : x E G} is a subgroup of H. o. Let's say anyway

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let G be a group with operation * and H be a group with operation º. Let's say anyway
f: G→ H is a mapping that has properties : Vx, y E G, apply
f(x * y) = f(x) • f (y)
O
f(x-¹) = f(x)-¹
●
show that
a) K = {x EG : f(x) = еµ} is a subgroup of G
e}
b) R = {f(x) EG : x E G} is a subgroup of H.
Transcribed Image Text:Let G be a group with operation * and H be a group with operation º. Let's say anyway f: G→ H is a mapping that has properties : Vx, y E G, apply f(x * y) = f(x) • f (y) O f(x-¹) = f(x)-¹ ● show that a) K = {x EG : f(x) = еµ} is a subgroup of G e} b) R = {f(x) EG : x E G} is a subgroup of H.
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