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Mathematics
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Mik
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i'm bad at math

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5
$G$ is a group, $H$ is a subgroup of $G$ such that $[G : H]=2$. Suppose $a, b \in G$, but neither $a$ nor $b$ are in $H$. Prove $ab \in H$.
Nov 20, 2013
5
Find a maximal ideal $I$ in the ring $\mathbb{Z}[i]$ such that $\mathbb{Z}[i]/I$ is isomorphic to $\mathbb{Z}/521\mathbb{Z}$.
Feb 18, 2014
4
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
Oct 3, 2013
4
$ G/N$ has an element of order $m$ so, $G$ also has an element of order $m$
Nov 15, 2013
3
Cayley's Theorem and group isomorphisms
Nov 26, 2013
2
Is this an equivalence relation?
Oct 2, 2013
2
Show that the integers have infinite index in the additive group of rational numbers.
Oct 28, 2013
2
Prove that the group G defined by a~b=a+b+ab is isomorphic to the multiplicative group of nonzero real numbers.
Nov 10, 2013
2
Prove that $S_n$ satisfies the following property: if $g \in S_n$, then $g$ and $g^{-1}$ are conjugate in $S_n$.
Nov 15, 2013
2
Suppose R is an integral domain. Prove that $(a)=(b)$ if and only if $b = ua$ where $u$ is in $R^\times$
Jan 27, 2014