Question

Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?

score 260 · Answer 1 · 2020-07-12 21:09:58

260

Views

Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?

Published on 12 Jul 2020 - 21:09

score 96 · Answer 2 · 2020-07-13 07:45:35

96

Views

Show that $\mathbb Z$ with operation $•$, $a•b =a+b$ if $a$ is even ; $a•b =a-b$ if $a$ is odd is a group.

Published on 13 Jul 2020 - 7:45

score 679 · Answer 3 · 2020-07-19 04:25:46

679

Views

Subgroup of a ring closed under multiplication?

Published on 19 Jul 2020 - 4:25

score 28 · Answer 4 · 2020-07-20 18:43:38

28

Views

Determine whether the given function $F(x,y) = x/y$ is as binary operation on the given set $A$

Published on 20 Jul 2020 - 18:43

score 42 · Answer 5 · 2020-07-21 01:23:15

42

Views

What is the restriction of $F(x,y)=(xy) - |x||y|$ to the set of all nonnegative real numbers?

Published on 21 Jul 2020 - 1:23

score 190 · Answer 6 · 2020-07-24 07:59:28

Additional condition needed for a binary operation to have inverse, apart from the necessary condition of having a two-sided identity.

score 47 · Answer 7 · 2020-07-30 07:04:43

47

Views

What are some less known pairs of binary operators on Integers are distributive?

Published on 30 Jul 2020 - 7:04

score 1.4k · Answer 8 · 2016-07-16 13:23:49

1.4k

Views

⋇ "Division Times" operator in Unicode (U+22C7)?

Published on 16 Jul 2016 - 13:23

score 295 · Answer 9 · 2026-03-26 08:04:27

295

Views

Does this particular axiom on a semigroup guarantee that it is a group?

Published on 26 Mar 2026 - 8:04

score 2.4k · Answer 10 · 2016-07-25 02:12:55

2.4k

Views

Why is Nim solvable with the xor operator?

Published on 25 Jul 2016 - 2:12

score 299 · Answer 11 · 2016-07-25 07:31:08

299

Views

Proving an idempotent binary operation where $(x\ast y)\ast z=(y\ast z)\ast x$ is commutative

Published on 25 Jul 2016 - 7:31

score 80 · Answer 12 · 2016-07-29 00:31:45

80

Views

Proof about binary structures and binary operations

Published on 29 Jul 2016 - 0:31

score 561 · Answer 13 · 2016-07-29 01:39:15

561

Views

Commutativity and associativity of isomorphic binary structures

Published on 29 Jul 2016 - 1:39

score 1k · Answer 14 · 2016-08-08 15:48:59

1k

Views

Define a binary composition ( operation ) $\star$ such that $\langle G,\star\rangle$ is a group with $a$ as its identity.

Published on 08 Aug 2016 - 15:48

score 7.8k · Answer 15 · 2016-08-25 17:44:01

7.8k

Views

Binary multiplication as combination of addition and left shift

Published on 25 Aug 2016 - 17:44

List Question

Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?

Show that $\mathbb Z$ with operation $•$, $a•b =a+b$ if $a$ is even ; $a•b =a-b$ if $a$ is odd is a group.

Subgroup of a ring closed under multiplication?

Determine whether the given function $F(x,y) = x/y$ is as binary operation on the given set $A$

What is the restriction of $F(x,y)=(xy) - |x||y|$ to the set of all nonnegative real numbers?

Additional condition needed for a binary operation to have inverse, apart from the necessary condition of having a two-sided identity.

What are some less known pairs of binary operators on Integers are distributive?

⋇ "Division Times" operator in Unicode (U+22C7)?

Does this particular axiom on a semigroup guarantee that it is a group?

Why is Nim solvable with the xor operator?

Proving an idempotent binary operation where $(x\ast y)\ast z=(y\ast z)\ast x$ is commutative

Proof about binary structures and binary operations

Commutativity and associativity of isomorphic binary structures

Define a binary composition ( operation ) $\star$ such that $\langle G,\star\rangle$ is a group with $a$ as its identity.

Binary multiplication as combination of addition and left shift

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