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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Can i use this definition to prove a set with an operator a group?
please send the solution to the problem given in the attachment.
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Alka gupta Best Answer
yes, this is defination of subgroup if we want to check a non empty subset of a group is subgroup of G....then we have to check a,b€H => ab^-1 €H
can I use this test to prove a nonempty set a group?
??
no...if we consider any nonempty set with a binary operation then we can not prove group by this result ....we have to check all four property of group ..( clouser , associative , identity , inverse )
if H is non empty subset of Group G then we can use this result to prove H is group
there must be a profound reason for that.