Converse of Lagrange Theorem for p-groups.
18181
Complete classification of the groups for which converse of Lagrange's Theorem holds
29802
Part of simple proof of nontrivial center in p-group
33294
The correspondence theorem for groups
46116
Proof of the First Isomorphism Theorem for Groups
133770
Subgroups of finite abelian groups.
99346
Prove a result on transitive group actions.
123796
Order of automorphism group of a $p$-group is divisible by $p$.
4402
Group of order $pqr$, $p < q < r$ primes
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
57427
Group of order $8p$ is solvable, for any prime $p$
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
91874
Existence of finite indexed normal subgroup for a given finite indexed subgroup.
44258
Conditions under which group solvability is invariant under an homomorphism.
7973
Groups of order $pq$ have a proper normal subgroup
44497
Can we equip the power set $P$ of any set $S$ with a binary operation such that $P$ becomes a group (with some restrictions)?
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
122970
A question on $p$-groups, and order of its commutator subgroup.