Every group of order 7 is
Show Hint
- not abelian
- not cyclic
- cyclic
- None of these
The Correct Option is C
Solution and Explanation
A fundamental result in group theory states that every group whose order is a prime number must be cyclic.
Step 2: Detailed Explanation:
The number 7 is prime. By Lagrange's theorem and the corollary for prime-order groups, every group of prime order $p$ is cyclic (generated by any non-identity element) and therefore also abelian.
Step 3: Final Answer:
Every group of order 7 is cyclic (and hence abelian).
Top MET Mathematics Questions
- If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then
- MET - 2019
- Mathematics
- Continuity
- The remainder obtained when \(5^{124}\) is divided by 124 is
- MET - 2019
- Mathematics
- Number Theory
- The adjoining graph
- MET - 2019
- Mathematics
- Graph Theory
- If \(I_n = \int \sin^n x dx\), then \(nI_n - (n - 1)I_{n-2}\) equals
- MET - 2019
- Mathematics
- Integral Calculus
- If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is
Top MET Algebra Questions
- In the group $G = \{0,1,2,3,4\}$ under $\times_5$, the inverse of $(2 \times_5 2^{-1})$ is}
- If $a * b$ denote the bigger among a and b and $a \cdot b = a + b + 3(a*b)$, then $4 \cdot 7$ is equal to
- If every element of a group G is its own inverse, then G is
- In the set $Q^+$ of all positive rational numbers, the operation $*$ is defined by the formula $a * b = \frac{ab}{6}$. Then, the inverse of $9$ with respect to $*$ is
Top MET Questions
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- MET - 2020
- Photoelectric Effect
- If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then
- MET - 2019
- Continuity
Helicopters are very different from airplanes. They can do three things that airplanes cannot do. First, when airplanes move upward, they must also move forward, but helicopters can move straight up without moving ahead. Second, helicopters can fly backward, which airplanes cannot do. Third, helicopters can use their rotors to hover in the air, which is impossible for airplanes. Helicopters can perform actions that airplanes cannot, they are used for different tasks. Since, helicopters can take off without moving forward, they do not need a runway for take off. They are used in congested areas where there is no room for airplanes or in isolated areas, which do not have airports. Because they can hover, they are used on firefighting missions to drop water on fires. They are used in logging operations to lift trees out of forests. Helicopters are used as air ambulances to airlift patients out of situations, which are difficult to reach by conventional ambulances. The police used helicopters to follow suspects on the ground or to search for cars on the ground. Of course, helicopters have military uses because of their design and capabilities.
- MET - 2019
- Reading Comprehension
- Find the missing character.
- MET - 2019
- Number Patterns
- 6, 9, 12, 15, 18, ?
- MET - 2019
- Number Patterns