True or False. If H is a subgroup of the group G then H is one of its cosets in G. Every
subgroup of a group G is normal. If |H|
Solution
a) True as He=H where e is identity element.
b) False, only the subgroup N satistfying the property gng^-1 in N for every n in N and g in G(
group) are normal.
but if group is abelian then every subgroup is normal.
c) True, as K contain more elements than H it has more subgroups.
d) False, For two distinct cosest identity elements belongs to only one cosets because distinct
cosets for set of equivalance classes.
e) yes for each positive integer n we have group for that number.
f) false, because it is only true only if G has order of prime power (sylow thm).
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
True or False. If H is a subgroup of the group G then H is one of it.pdf
1. True or False. If H is a subgroup of the group G then H is one of its cosets in G. Every
subgroup of a group G is normal. If |H|
Solution
a) True as He=H where e is identity element.
b) False, only the subgroup N satistfying the property gng^-1 in N for every n in N and g in G(
group) are normal.
but if group is abelian then every subgroup is normal.
c) True, as K contain more elements than H it has more subgroups.
d) False, For two distinct cosest identity elements belongs to only one cosets because distinct
cosets for set of equivalance classes.
e) yes for each positive integer n we have group for that number.
f) false, because it is only true only if G has order of prime power (sylow thm)
