2 votes 2 votes closed as a duplicate of: maths_mocktest1_30 Let G be a finite group.If A and B are subgroups of G with orders 4 and 5 respectively then |A$\cap$B|=...... Set Theory & Algebra group-theory discrete-mathematics + – junaid ahmad asked Nov 18, 2017 • closed Nov 28, 2017 by LeenSharma junaid ahmad 1.2k views comment Share Follow See all 5 Comments See all 5 5 Comments reply joshi_nitish commented Nov 18, 2017 reply Follow Share |A∩B|=1 intersection property of group says that -> intersection of two subgroups G1 and G2 of a group G is a subgroup of both the groups G1 and G2. 1 is only common factor of 4 and 5 8 votes 8 votes hs_yadav commented Nov 18, 2017 reply Follow Share joshi_nitish is it means only one element would be common in A and B and that is identity element...?? 0 votes 0 votes joshi_nitish commented Nov 18, 2017 reply Follow Share yes. 0 votes 0 votes abhishek tiwary commented Nov 19, 2017 reply Follow Share for satisfied the properties of SUBGROUP 1 closure,2 identity 3 inverse should satisfy for intersection of any no of SUBGROUP of a GROUP identity element should be common 0 votes 0 votes junaid ahmad commented Nov 19, 2017 reply Follow Share @abhishek tiwary when you take the intersection of two subgroups,which in fact also a subgroup.so you don't really need to prove again all the properties. 0 votes 0 votes Please log in or register to add a comment.