The multiplicative group $\left( \mathbb{Z}/n\mathbb{Z}\right)^*$ is defined by : $ \left( \mathbb{Z}/n\mathbb{Z}\right)^*= \{\, \bar{x} \in \mathbb{Z}/n\mathbb{Z}\;\;:\;\;gcd(x,n)=1 \,\} $ then we have : $$ \left( \mathbb{Z}/50\mathbb{Z}\right)^*= \{\, \bar{1},\bar{3},\bar{7},\bar{9},\bar{11},\bar{13},\bar{17},\bar{19},\bar{21},\bar{23},\bar{27},\bar{29},\bar{31},\bar{33},\bar{37} ,\bar{39},\bar{41},\bar{43},\bar{47},\bar{49} \,\} $$ then the set $$\mathbb{E} = \{\,\bar{1},\bar{11},\bar{21},\bar{31},\bar{41} \,\}$$ is a subgroup of the multiplicative group $\left( \mathbb{Z}/n\mathbb{Z}\right)^*$ , the question now , is there are a method to build the subgroup of $\left( \mathbb{Z}/n\mathbb{Z}\right)^*$ for every integer not null ??
2026-03-25 18:48:35.1774464515
is there are a method to build subgroups of the multiplicative group $\left( \mathbb{Z}/n\mathbb{Z}\right)^*$
77 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in ARITHMETIC
- Solve this arithmetic question without algebra
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- Upper bound for recursion?
- Proving in different ways that $n^{n-1}-1$ is divisible by $(n-1)^2$.
- Meaning of a percentage of something
- Compare $2^{2016}$ and $10^{605}$ without a calculator
- The older you are, the richer you get?
- Easy question which doesn't make sense to me!
- Calculating diminishing interest amount
- Multiplication Question
Related Questions in TOTIENT-FUNCTION
- Reciprocal-totient function, in term of the totient function?
- A congruence with the Euler's totient function and sum of divisors function
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- For which natural numbers are $\phi(n)=2$?
- A congruence with the Euler's totient function and number of divisors function
- Does converge $\sum_{n=2}^\infty\frac{1}{\varphi(p_n-2)-1+p_n}$, where $\varphi(n)$ is the Euler's totient function and $p_n$ the $n$th prime number?
- On the behaviour of $\frac{1}{N}\sum_{k=1}^N\frac{\pi(\varphi(k)+N)}{\varphi(\pi(k)+N)}$ as $N\to\infty$
- On the solutions of an equation involving the Euler's totient function that is solved by the primes of Rassias' conjecture
- Are there any known methods for finding Upper/Lower bounds on the number of Totients of x less than another number y?
- How is Carmichael's function subgroup of Euler's Totient function?
Related Questions in MAXIMAL-SUBGROUP
- Number of nonidentity Elements Contained in Conjugates of $M$
- Generating Prüfer 2-group without its Frattini Subgroup
- $G$ is a group of order $pq$ and $P_q$ and $P_p$ are Sylow subgroups...
- $(\mathbb{Q},+)$ has no maximal subgroup.
- Example of a group where a proper subgroup is not included in a maximal element
- Prove $\hat{G}\rtimes Aut(G)$ is primitive when $G$ is characteristically simple
- How can we describe all maximal proper subgroups of $G \times G$
- Why $a,b$ assumed coprime?
- Why does ergodicity fail?
- Intersection of all maximal subgroups of a finite group
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?