I have constructed (as a permutation group on 121 points) a Frobenius group of order (121)(120) with kernel K = $C_{11}^2$ and cyclic complement H of order 120. I have checked its properties very carefully, and also asked a colleague (an algebraist and professor of mathematics in North Carolina) to double-check it for me. He input my data to a program designed for group calculations, confirming it as a Frobenius group. There can be no mistake. Yet I understand there is a Frobenius group of this order and this kernel whose complement is not cyclic. Either there are two such non-isomorphic groups (which I believe is impossible) or the latter group does not exist. Can anyone point me to an authoritative reference that resolves this question?
2026-02-23 06:24:26.1771827866
What reference books or papers address Frobenius groups: in particular, of order (121)(120)?
59 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 FROBENIUS-GROUPS
- No of elements in a subgroup of the Galois group.
- Frobenius group and conjugacy relation
- What are the Frobenius groups of order $100$?
- Use of frobenius map of an elliptic curve
- Why the normalizer of the Sylow $p$-subgroups of the symmetric group of degree $p$ has order $p(p-1)$ and is known as Frobenius group $F_{p(p-1)}$?
- Frobenius coin problem induction help
- On groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
- on primitive group actions with abelian stabilizers
- How to reconstruct geometric object that a Frobenius group acts on
- Differential equation with zero solution of indicial equation?
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?