The intersection of subgroups of finite p-groups

2010 ◽  
Vol 96 (1) ◽  
pp. 9-17 ◽  
Author(s):  
Qinhai Zhang ◽  
Junjun Wei
Keyword(s):  
Intersection Of Subgroups

scholarly journals On a conjecture of Imrich and Müller

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Sergei V. Ivanov
Keyword(s):  
Free Groups ◽  
Intersection Of Subgroups

AbstractA conjecture of Imrich and Müller on the rank of the intersection of subgroups of free groups is disproved.

scholarly journals INTERSECTION OF SUBGROUPS IN FREE GROUPS AND HOMOTOPY GROUPS

2008 ◽  
Vol 18 (05) ◽  
pp. 803-823 ◽  
Author(s):  
HANS-JOACHIM BAUES ◽  
ROMAN MIKHAILOV
Keyword(s):  
Abelian Group ◽  
Free Group ◽  
Homotopy Group ◽  
Homotopy Groups ◽  
Natural Homomorphism ◽  
Two Dimensional ◽  
The Third ◽  
Cw Complex ◽  
Intersection Of Subgroups ◽  
The Right

We show that the intersection of three subgroups in a free group is related to the computation of the third homotopy group π3. This generalizes a result of Gutierrez–Ratcliffe who relate the intersection of two subgroups with the computation of π2. Let K be a two-dimensional CW-complex with subcomplexes K1, K2, K3 such that K = K1 ∪ K2 ∪ K3 and K1 ∩ K2 ∩ K3 is the 1-skeleton K1 of K. We construct a natural homomorphism of π1(K)-modules [Formula: see text] where Ri = ker {π1(K1) → π1(Ki)}, i = 1,2,3 and the action of π1(K) = F/R1R2R3 on the right-hand abelian group is defined via conjugation in F. In certain cases, the defined map is an isomorphism. Finally, we discuss certain applications of the above map to group homology.

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