Question

Prove that there are no idempotent, commutative quasigroups of even order.

score 348 · Answer 1 · 2026-02-22 23:10:49

348

Views

Prove that there are no idempotent, commutative quasigroups of even order.

Published on 22 Feb 2026 - 23:10

score 94 · Answer 2 · 2026-02-22 23:12:31

94

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Is there any name for this property of quasigroups: $x \times (y \times (z \times t)) = (x \times y) \times (t \times z)?$

Published on 22 Feb 2026 - 23:12

score 607 · Answer 3 · 2026-02-22 23:09:15

607

Views

What is the difference between quasigroup with associativity and semigroup with inverse?

Published on 22 Feb 2026 - 23:09

score 112 · Answer 4 · 2026-02-22 23:07:19

112

Views

Prove that a map is not quasi-isometric embedding

Published on 22 Feb 2026 - 23:07

score 102 · Answer 5 · 2026-04-08 23:40:17

102

Views

Composition Law to make a Quasigroup

Published on 08 Apr 2026 - 23:40

score 32 · Answer 6 · 2026-03-22 08:50:24

32

Views

Salzmann's topological loop example

Published on 22 Mar 2026 - 8:50

score 53 · Answer 7 · 2026-02-22 23:07:16

53

Views

Term for a Set Equipped With a Binary Operation Which Contains Inverses

Published on 22 Feb 2026 - 23:07

score 982 · Answer 8 · 2026-02-22 23:08:48

982

Views

What are the commutative quasigroups satisfying $a/b=b/a$?

Published on 22 Feb 2026 - 23:08

score 754 · Answer 9 · 2026-02-22 23:12:17

754

Views

The unique loop (quasigroup with unit) $L$ of order $5$ satisfying $x^2 = 1$ for all $x \in L$

Published on 22 Feb 2026 - 23:12

score 111 · Answer 10 · 2026-02-22 23:10:58

111

Views

What is the meaning of division for quasigroups in here?

Published on 22 Feb 2026 - 23:10

score 837 · Answer 11 · 2026-03-22 17:38:55

837

Views

Looking for examples of finite loops and monoids

Published on 22 Mar 2026 - 17:38

score 149 · Answer 12 · 2026-02-22 23:10:48

149

Views

A familiar quasigroup - about independent axioms

Published on 22 Feb 2026 - 23:10

score 111 · Answer 13 · 2026-02-22 23:05:52

111

Views

A simple question about rational numbers without a simple proof?

Published on 22 Feb 2026 - 23:05

score 128 · Answer 14 · 2026-02-22 23:07:19

128

Views

Does every non-empty quasigroup have a left or right identity?

Published on 22 Feb 2026 - 23:07

score 132 · Answer 15 · 2026-02-22 23:12:33

132

Views

If $H$ is a subloop of a finte loop $L$ and $N$ is a normal subloop of $L$, then $HN$ is a subloop of $L$.

Published on 22 Feb 2026 - 23:12

List Question

Prove that there are no idempotent, commutative quasigroups of even order.

Is there any name for this property of quasigroups: $x \times (y \times (z \times t)) = (x \times y) \times (t \times z)?$

What is the difference between quasigroup with associativity and semigroup with inverse?

Prove that a map is not quasi-isometric embedding

Composition Law to make a Quasigroup

Salzmann's topological loop example

Term for a Set Equipped With a Binary Operation Which Contains Inverses

What are the commutative quasigroups satisfying $a/b=b/a$?

The unique loop (quasigroup with unit) $L$ of order $5$ satisfying $x^2 = 1$ for all $x \in L$

What is the meaning of division for quasigroups in here?

Looking for examples of finite loops and monoids

A familiar quasigroup - about independent axioms

A simple question about rational numbers without a simple proof?

Does every non-empty quasigroup have a left or right identity?

If $H$ is a subloop of a finte loop $L$ and $N$ is a normal subloop of $L$, then $HN$ is a subloop of $L$.

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