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List Question

Group of square free order with a normal $p$-Sylow is solvable

Visualization of groups with a normal subgroup

Prove that there is $x \in G$ such that $x \notin H, x^2 \notin H,...,x^{p - 1} \notin H$ but $x^p \in H$.

Let $G$ be Abelian. Then any subgroup of $G$ is normal. Does the converse hold?

$H/K$ when $K$ is not a subgroup of $H$.

Is there a way to classify all finite groups $G$, such that $\pi(G) := \Pi_{H \triangleleft G} |H| = |G|^2$?

Deck Transformations Question

$H \triangleleft G$, $h \in H$. $C_G(h)g \cap H \ne \emptyset, \forall g \in G$ implies $\lbrace C_G(h)g \cap H, g \in G \rbrace$ partition of $H$?

Locus equation in a non-simple group

Group Homomorphisms into an Abelian Group

How to show that $C_G(a)=N_G(a)$?

Locus equation in a non-simple group_part#2

If $aH=bH \implies Ha=Hb$ for a subgroup H having finite index, then $gH=Hg$ for all $g \in G$?

The elements of a matrix group with order two and its centre

Visualization of groups with a normal subgroup_rev#1

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