Show that every solvable group of order $360$ has a subgroup of order 90. (This is straightforward if you use the Philip Hall theorems. Is there an easy proof that doesn't use them?)
2026-02-22 21:03:02.1771794182
Groups of Order 360
197 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in FINITE-GROUPS
- List Conjugacy Classes in GAP?
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- Assuming unitarity of arbitrary representations in proof of Schur's lemma
- existence of subgroups of finite abelian groups
- Online reference about semi-direct products in finite group theory?
- classify groups of order $p^2$ simple or not
- Show that for character $\chi$ of an Abelian group $G$ we have $[\chi; \chi] \ge \chi(1)$.
- The number of conjugacy classes of a finite group
- Properties of symmetric and alternating characters
- Finite group, How can I construct solution step-by-step.
Related Questions in SYLOW-THEORY
- A group of order 189 is not simple
- classify groups of order $p^2$ simple or not
- Proof verification - the only group of order 24 without normal sylow subgroup is $S_4$.
- Calculating the index of a subgroup containing the normalizer of a Sylow $p$ subgroup
- If $|G| = p^nq$ then $G$ has only one normal subgroup of order $q$
- Classify all groups of order 75
- Group of order 616 solvable?
- Could we get any information from about class equation from index of sylow subgroups
- Second part of Sylow's Theorem about conjugacy
- If $G$ is non-abelian and simple then $|G|$ divides $n_p!/2$
Related Questions in SOLVABLE-GROUPS
- If $H$ and $K$ are solvable subgroups of $G$ with $H\unlhd G $ then $HK$ is a solvable subgroup of $G .$
- Cannot follow proof that refinement of solvable series is also solvable
- Group of order 616 solvable?
- The bound for $p$-length of $p$-solvable group
- The context & motivation for the Tits alternative in combinatorial group theory
- Is every group $G$ such that $\bigcap\limits_nG^{(n)}$ is trivial, solvable?
- Jordan -Holder for infinite series? composition series $\rightarrow$ chief series
- Solvable group, primitive group action
- Every group of order 300 is solvable?
- Compositum of solvable extensions
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?