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Abelian groups about rationals
Exact sequence of abelian groups, property transfersNon-Abelian groups and subgroupsIn direct products of $n$ groups, do we also prove conditions for a group to be abelian or not?Question about finitely generated abelian groupsQuestion about Finite Abelian GroupsAbstract Algebra. Let $mathitG $ be an abelian group. Show that the elements of finite order in $mathitG$ form a subgroup of $mathitG$.True or false simple algebra questions (centralizers, conjugacy classes, normal groups, abelian groups)Abelian groups of odd orderAbelian Group of Rationals over addition - axiomatic or derived?Showing there is a unique group table for $1, a,b,c$ such that there is no element of order $4$.
$begingroup$
Is the set $mathbbQ$ under $×$ an abelian group? It is sure for $mathbbQ - 0$, but i think the whole set of rationals is not an abelian group as $0 × a = a × 0 = 0$, but the identity element is $1$ and i think it must be unique, and $a$ is not equal to $0$. Can you please help me whether it is an abelian group under $×$ or not?
abstract-algebra abelian-groups rational-numbers binary-operations
edited Apr 3 at 3:00
user21820
40.1k544162
$endgroup$
add a comment |
$begingroup$
Is the set $mathbbQ$ under $×$ an abelian group? It is sure for $mathbbQ - 0$, but i think the whole set of rationals is not an abelian group as $0 × a = a × 0 = 0$, but the identity element is $1$ and i think it must be unique, and $a$ is not equal to $0$. Can you please help me whether it is an abelian group under $×$ or not?
abstract-algebra abelian-groups rational-numbers binary-operations
edited Apr 3 at 3:00
user21820
40.1k544162
$endgroup$
add a comment |
$begingroup$
Is the set $mathbbQ$ under $×$ an abelian group? It is sure for $mathbbQ - 0$, but i think the whole set of rationals is not an abelian group as $0 × a = a × 0 = 0$, but the identity element is $1$ and i think it must be unique, and $a$ is not equal to $0$. Can you please help me whether it is an abelian group under $×$ or not?
abstract-algebra abelian-groups rational-numbers binary-operations
edited Apr 3 at 3:00
user21820
40.1k544162
$endgroup$
Is the set $mathbbQ$ under $×$ an abelian group? It is sure for $mathbbQ - 0$, but i think the whole set of rationals is not an abelian group as $0 × a = a × 0 = 0$, but the identity element is $1$ and i think it must be unique, and $a$ is not equal to $0$. Can you please help me whether it is an abelian group under $×$ or not?
abstract-algebra abelian-groups rational-numbers binary-operations
abstract-algebra abelian-groups rational-numbers binary-operations
edited Apr 3 at 3:00
user21820
40.1k544162
edited Apr 3 at 3:00
user21820
40.1k544162
edited Apr 3 at 3:00
user21820
40.1k544162
edited Apr 3 at 3:00
user21820
40.1k544162
edited Apr 3 at 3:00
user21820
40.1k544162
40.1k544162
asked Mar 22 at 16:14
user655794
add a comment |
add a comment |
1 Answer
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$begingroup$
It is not a group under multiplication, since $0$ has no inverse.
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
add a comment |
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1 Answer
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1 Answer
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active
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votes
$begingroup$
It is not a group under multiplication, since $0$ has no inverse.
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
add a comment |
$begingroup$
It is not a group under multiplication, since $0$ has no inverse.
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
add a comment |
$begingroup$
It is not a group under multiplication, since $0$ has no inverse.
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
$endgroup$
It is not a group under multiplication, since $0$ has no inverse.
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
answered Mar 22 at 16:15
José Carlos SantosJosé Carlos Santos
173k23133241
173k23133241
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
add a comment |
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
$begingroup$
Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete?
$endgroup$
– user655794
Mar 25 at 19:15
add a comment |
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