Show that the following two conditions on a group G are equivalent:(1) There is a homomorphism o from G into E, such that (g) +1 forsome g e G.(2) The group G contains a proper subgroup of index at most n.

We have to prove that the following two conditions on a group G are equivalent : (1) There is a…

Answered: Show that the following two conditions…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 12E

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Show that the following two conditions on a group G are equivalent: homomorphism p from G into Σ, such that p(g) + 1 for 4 (1) There is a some g € G. (2) The group G contains a proper subgroup of index at most n.