0 votes 0 votes Let $G$ be a finite group with sub group $H$ & $K$ such that $|H|=7$ and $|K|=31$ then find $| H ⋂ K|$ Set Theory & Algebra engineering-mathematics set-theory&algebra set-theory + – Deepesh Pai asked Mar 6, 2018 • retagged Mar 8, 2018 by Sukanya Das Deepesh Pai 409 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply rahul sharma 5 commented Mar 6, 2018 reply Follow Share 1? As | H intersection K| should divide order of hours as well as k and as h and k are prime. So only. Number that divides is 1 0 votes 0 votes Mk Utkarsh commented Mar 7, 2018 reply Follow Share yes if two subgroups are mutually prime then there intersection is 1 and that element is identity. 0 votes 0 votes Akhilesh Singla commented Mar 7, 2018 reply Follow Share Yeah, it must be 1. 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes As, $gcd(7,31) = 1$ then, $|H⋂K| = 1$ Sukanya Das answered Mar 8, 2018 Sukanya Das comment Share Follow See all 0 reply Please log in or register to add a comment.