All Questions
Tagged with magma group-theory
30
questions
2
votes
0
answers
28
views
Weaker notion of closure for partial magmas
Let $(G,\cdot)$ be a partial magma (a set endowed with a partial binary operation). In principle, for such generic structures it is possible that $\exists g \in G$ such that $\forall h \in G, \, g\...
-1
votes
1
answer
43
views
map from spin to special orthogonal in Magma [closed]
Let $G:=\operatorname{Spin}(7,5)$. How to construct in Magma the map $G \rightarrow G/Z(G) $ where $Z(G)$ is the center. I get this from Magma:
...
- 1,303
-4
votes
1
answer
79
views
Practical example of differences between associativity and alternativity (and the in-between Bol loop)? [closed]
Associativity is:
$$(a * b) * c = a * (b * c)$$
Alternativity is:
$$a * (a * b) = (a * a) * b$$
$$(a * b) * b = a * (b * b)$$
Bol loop is:
$${\displaystyle a(b(ac))=(a(ba))c}$$
$${\displaystyle ((ca)b)...
- 3,773
0
votes
1
answer
55
views
Term for a Set Equipped With a Binary Operation Which Contains Inverses
Let $A$ be a set and let $\circ:A\times A\rightarrow B,$ $A\subseteq B$ be a binary operation ($A$ is not necessarily closed under $\circ$). If there exists some unique $e\in A$ such that $e\circ a=a\...
- 491
2
votes
1
answer
176
views
How to show that a compact semigroup for which the cancellation law holds is a compact group
Here is my problem:
Set $G$ a compact semigroup (that is a Hausdorff compact space endowed with an associative continuous binary operation). Assume that the cancellation law holds i.e. for any $g,h,k \...
- 166
2
votes
2
answers
268
views
Faithful permutation representation
excuse me if my question is trivial.
I’m trying to use magma to construct faithful permutation representations of a certain group using the group action that lets the group G acts by the left ...
- 23
3
votes
2
answers
169
views
How many non-isomorphic algebraic structures (i.e. magmas, monoids, groups etc.) are there with countably infinite order? [closed]
For structures of finite order it seems obvious to me that there are countably infinite in total, by a simple diagonalization argument (starting at all of order 1, then 2 etc.). It is however not ...
- 462
2
votes
2
answers
199
views
What is the name for a magma which is neither a quasigroup nor a semigroup yet has both an identity and inverses?
Is there a name which is more specific than `unital magma' for a magma whose only requirements are that it should have both an identity and (L/R symmetric) inverses for all elements?
The following ...
- 407
5
votes
0
answers
204
views
Suspicious diagrams on wiki about group-like structures
It seems to me that the diagrams on wiki about group-like structures are not quite right. For example, the following
https://en.wikipedia.org/wiki/Monoid#/media/File:Algebraic_structures_-...
- 274
7
votes
2
answers
551
views
Defining loops: why is divisibility and identitiy implying invertibility?
Wikipedia contains the following figure (to be found, e.g. here) in order to visualize the relations between several algebraic structures. I highlighted a part that I find especially interesting.
It ...
- 30.1k
5
votes
1
answer
173
views
Computing the number of conjugacy-classes in $GL_{n}(\mathbb{F}_{p})$ of elementary abelian p-subgroups by GAP and Magma
I'm trying to compute the number of conjugacy-classes of elementary abelian p-subgroups of rank $2$ in $GL_{n}(\mathbb{F}_{p})$ by GAP and Magma. So I consider the following GAP function:
...
3
votes
1
answer
394
views
Is every group isomorphic to the automorphism group of some magma?
I believe that magma isomorphism is defined as $\phi(x*y)=\phi(x)*'\phi(y)$. The automorphism group is the set of bijective isomorphisms from the elements of the magma to itself, under the operation ...
- 1,635
3
votes
7
answers
122
views
Is $G = (\Bbb Q^*,a*b=\frac{a+b}{2})$ a group, monoid, semigroup or none of these?
Is $G = (\Bbb Q^*,a*b=\frac{a+b}{2})$ a group, monoid, semigroup or none of these?
I tried to solve it by assuming $ a,b,c \in G $ such that $a*(b*c)=(a*b)*c$. Then$$\frac{a+\frac{b+c}{2}}{2} = \frac{...
- 189
0
votes
2
answers
41
views
Valid reason to prove the dis-associativity of ($\mathbb R, -)$.
Is this a valid proof?
Let $a,b,c$ $\in$ $(\mathbb R, -)$. We want to prove that $(\mathbb R, -)$ does not have an associative property. Assume that it is associative such that: $a-(b-c) = (a-b)-c$.
$...
- 52
1
vote
0
answers
77
views
Reference Request: An operation preserving bijection from a magma to a group must be a group isomorphism
Let $M$ be a magma with a binary operation $*_M$ and let $G$ be a group with a binary operation $*_G$.
If $f$ is a bijection from $M$ to $G$ preserving the operation,
that is, $f(m_1 *_M m_2)=f(m_1)...
- 3,771