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1d
comment When does normal maximal subgroup have prime index?
But is the proper subgroup normal? See the remark of Qiaochu Yuan!
2d
awarded  group-theory
Feb
9
revised Abelian subgroup of standard wreath product
edited title
Feb
8
comment If commutativity of vector space is omitted, can we still use other axioms to prove the commutativity?
@Pedro, yes, the ring $R$ is an $R$-module over itself!
Feb
8
comment $G$ a finite group such that $x^2 = e$ for each $x$ implies $G \cong \mathbb{Z}_2 \times … \times \mathbb{Z}_2$ ($n$ factors)
It helps if you first show that $G$ has to be abelian: $(xy)^2=xyxy=e=x^2y^2$ ...
Feb
8
comment If commutativity of vector space is omitted, can we still use other axioms to prove the commutativity?
Yes exactly, in characteristic $2$, $(x+y)+(x+y)=0=(x+x)+(y+y)$, so same reasoning.
Feb
8
answered If commutativity of vector space is omitted, can we still use other axioms to prove the commutativity?
Feb
8
comment If $a$ is the only element of order $2$ in a group, show that $a$ is in the center of the group.
OK Zachary, well done. I will give you another one to think about: let $G$ be a group with a unique element of order $n \gt 1$. Then $n=2$.
Feb
8
answered If $a$ is the only element of order $2$ in a group, show that $a$ is in the center of the group.
Feb
8
comment If $H \triangleleft K \leqslant G$, which requirements must be placed on $K$ in order to obtain $N \triangleleft G$?
$G'$ is the commutator subgroup of $G$.
Feb
8
answered If $H \triangleleft K \leqslant G$, which requirements must be placed on $K$ in order to obtain $N \triangleleft G$?
Feb
8
answered Question regarding the normality of a certain subgroup of a group
Feb
8
comment Intersection of subgroup with Sylow subgroup
Rather look at $|HP:H|=|P:H \cap P|$, since $H \unlhd HP$. $P$ does not have to be normal.
Feb
8
comment Intersection of subgroup with Sylow subgroup
In general this is not true, but if $H$ is normal it is true.
Feb
7
answered Prove or give a counterexample: If a group G has a subgroup of order n, then G has an element of order n
Feb
6
answered If $\gcd(a, c) = 1$ and $b | c$, prove that $(a, b) = 1$
Feb
6
reviewed Reject How can I prove that only there continuous odd prime are $3,5,7$?
Feb
5
revised Let A and B be ideals of a ring and C a prime ideal. Prove if the intersection of A and B is a subset of C then either A or B is a subset of C
deleted 13 characters in body
Feb
5
answered How can I prove that only there continuous odd prime are $3,5,7$?
Feb
5
revised Calculate $\sqrt{x^2+y^2+2x-4y+5} + \sqrt{x^2+y^2-6x+8y+25}$, if $3x+2y-1=0$
added 13 characters in body