User MathStudent101

MathStudent101

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Jun 11
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group-theory

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solution-verification

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linear-algebra

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Let $n \in \mathbb {N}$ and $G$ a group of order $4n+2$. Prove $G$ isn't simple.

Jun 7

Let $T\colon V\to V$ over the IPS $V$ and $B$ be an orthogonal basis for $V$. Find the simplest connexion between $[T^*]_B$ and $([T]_B)^*$

May 25

Find how many $\tau \in S_{12}$ satisfy $\sigma \tau = \tau \sigma$ for $\sigma = (1\;9\;7\;10\;12\;2\;5)(4\;11)(3\;6\;8) \in S_{12}$

May 26

Prove/disprove: Let $G$ s.t $|G| = p^3 \implies |G'| \leq p$. [duplicate]

Aug 19

Prove two functions on an inner product space $S,T: V \to V$ are linear

May 25

Let $f:[0,1] \to \mathbf {R}$, continuous and $f(0)=f(1)$. Prove $f(x)=f(x+\frac{1}{2})$ has a solution $x_0 \in [0,\frac{1}{2}]$

May 28

Let $f:[0,1] \to \mathbb R$ differentiable s.t $f(0)=0$. $\forall x \in [0,1]$: $|f^{'}(x)| \le |f(x)|$. Prove $f(x) =0$, $\forall x \in [0,1]$.

Jun 10

A cyclic group of order 25 doesn't have an automorphism of order 3.

Aug 10

Let $V$ an inner product space and $T:V \to V$ a linear transformation. Prove $\operatorname{Ker} (T^*T)=\operatorname{Ker} T$

May 26

Let $G$ a simple group. Suppose exists a conjugacy class $C$ in $G$ such that $C \neq$ {e} is finite. Prove G is finite.

May 26