4 votes 4 votes Which of the following is/are NOT a group? The integers under addition The nonzero integers under multiplication The nonzero real numbers under multiplication The complex numbers under addition Set Theory & Algebra goclasses2024-dm-3-weekly-quiz goclasses set-theory&algebra group-theory multiple-selects 1-mark + – GO Classes asked Apr 27, 2022 • retagged May 4, 2023 by Lakshman Bhaiya GO Classes 516 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Pranavpurkar commented Jan 16, 2023 reply Follow Share @Deepak Poonia Sir,under addition , set of complex numbers forms an abelian group.is this statement correct? 0 votes 0 votes Deepak Poonia commented Jan 17, 2023 reply Follow Share under addition , set of complex numbers forms an abelian group. is this statement correct? @Pranavpurkar Yes. Complex Numbers under Addition form an Abelian Group The structure (C,+) is an infinite abelian group. 1 votes 1 votes Pranavpurkar commented Jan 17, 2023 reply Follow Share @Deepak Poonia Thankyou sir! 0 votes 0 votes Please log in or register to add a comment.
4 votes 4 votes The nonzero integers under multiplication is not a group as there is no inverse of any element other than $1,-1.$ GO Classes answered Apr 27, 2022 GO Classes comment Share Follow See all 3 Comments See all 3 3 Comments reply abhirupray14 commented Oct 9, 2022 i edited by abhirupray14 Oct 14, 2022 reply Follow Share @GO Classes , I think option (d) is also correct because if 2 + i and 2- i are the complex numbers and if they are added then result is coming as 4 which is not complex number at all . So dissatisfying closure property . Therefore option (d) is also not a group. 1 votes 1 votes BHOJARAM commented Oct 17, 2022 reply Follow Share @GO Classes… please review the option d….addition of two complex numbers can be an integer also 0 votes 0 votes Deepak Poonia commented Oct 19, 2022 reply Follow Share Every Real number is also a Complex number. $4 = 4 + 0i$ $2i = 0 + 2i$ 4 votes 4 votes Please log in or register to add a comment.
