Course Code mth312 Question A ring (R, +,.) is a commutative ring with unity Answer if it is a commutative ring and has the multiplicative identity element Question Ring (R, +,.) is a ring with identity, if R has an identity element with respect to Answer Multiplication Question A set {0} is a ring with respect to the usual addition and multiplication called Answer trivial ring Question If a and b are integers, then Answer a is congruent to b modulo n if a-b is divisible by n Question Other (Z24) = 24, then \(Z_{24}\) Answer a Sylow 2-subgroup and a Sylow 3-subgoup Question Every group of order 20 has a Answer proper normal non-trivial subgroup Question Find the Sylow 5-subgroups of group G of order 255 Answer 1 or 51 Question Let H and K be normal subgroups of a group G, G is called the internal direct product of H and K if Answer \(G = HK and H\cap K=\left \{e}{ \right \}\) Question The possible disjoint products of two transpositions on \(A_{4}\) are Answer (1 2) (3 4), (1 3 ) (4 2), (1 4) (2 3) Question Find the order of \(A_{4}\) Answer 12 Question A ring (R, +,.) is a commutative ring with unity Answer if it is a commutative ring and has the multiplicative identity element Question A set {0} is a ring with respect to the usual addition and multiplication called Answer trivial ring Question If a and b are integers, then Answer a is congruent to b modulo n if a-b is divisible by n Question Other (Z24) = 24, then \(Z_{24}\) Answer a Sylow 2-subgroup and a Sylow 3-subgoup Question Every group of order 20 has a Answer proper normal non-trivial subgroup Question Find the Sylow 5-subgroups of group G of order 255 Answer 1 or 51 Question Let H and K be normal subgroups of a group G, G is called the internal direct product of H and K if Answer \(G = HK and H\cap K=\left \{e}{ \right \}\) Question The possible disjoint products of two transpositions on \(A_{4}\) are Answer (1 2) (3 4), (1 3 ) (4 2), (1 4) (2 3) Question Find the order of \(A_{4}\) Answer 12 Try Another Search