Mon, April 18, 2022
Public Access Category: All |
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- Time:
- 11:30am
- Description:
- Title: Commutators and commutator subgroups in finite p-groups.
Speaker : Rahul Kaushik
Time : 11:30-12:30
Date : 18th April (Monday)
Link : https://meet.google.com/bmi-aoav-tgi?authuser=0
Titile:
Commutators and commutator subgroups in finite p-groups
Let G be a finite group and K(G) := {[a, b] | a, b ∈ G}. It is well known that
the commutator subgroup γ2(G) of G is generated by K(G). A natural question that has attracted the attention of many mathematicians over last many decades is whether γ2(G) is equal to K(G) or not for groups G in a given class of groups.
Ore Conjectured that K(G) = γ2(G) for all finite simple groups G(proved in 2010).
This problem has been studied for different classes of groups. Our interest here is in
the groups of prime power order. It is planned, in this talk, to survey some relevant
literature and present our work along the above mentioned theme. We will give
a classification of finite p-groups G having γ2(G) of order p4 and exponent p such
that K(G) 6= γ2(G). Along with this we also present a complete characterisation of groups G of order p7 for which K(G) 6= γ2(G), and indicate further research directions suggested by our work.