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Recent questions tagged p190

Show that the set $ G = \{2^n / n \in Z\} $ is an abelian group under multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set of all matrices of the form $\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $, $a \in R$ − {0} forms an abelian group under matrix multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the order of each element in the group $ (Z_5 − \{[0]\}, _.5)$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set {[1], [3], [4], [5], [9]} forms an abelian group under multiplication modulo 11.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set G of all rational numbers except − 1 forms an abelian group with respect to the operation $$ given by $a b = a + b + ab$ for all $a, b \in G$.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set M of complex numbers z with the condition | z | = 1 forms a group with respect to the operation of multiplication of complex numbers.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that { $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega & 0 \\ 0 & \omega^2\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega^2 & 0 \\ 0 & \omega\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega^2\\ \omega & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega\\ \omega^2 & 0\end{smallmatrix} \bigr) $} where $\omega^3 = 1, \omega \neq 1$ form a group with respect to matrix multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set G of all positive rationals forms a group under the composition $$ defined by $a b = (\large\frac{ab}{3})$ for all $a, b \in G.$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Prove that the matrices $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr) $ form a group under matrix multiplication

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. Is it a monoid under each of the above operations?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set N of natural members is a semi-group under the operation $x * y $= max {x, y}. Is it a monoid?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let $S$ be a non-empty set and o be a binary operation on $S$ defined by $xoy = x ; x, y \in S$. Determine whether o is commutative and associative.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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