The direct product theorem for profinite groups

2006 ◽  
Vol 9 (3) ◽  
Author(s):  
Daniel Goldstein ◽  
Robert M Guralnick
Keyword(s):  
Direct Product ◽  
Product Theorem ◽  
Profinite Groups

scholarly journals A generalized Goursat lemma

2015 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Kristine Bauer ◽  
Debasis Sen ◽  
Peter Zvengrowski
Keyword(s):  
Finite Number ◽  
Direct Product ◽  
Profinite Groups ◽  
Infinite Groups ◽  
Cyclic Groups

Abstract In this note the usual Goursat lemma, which describes subgroups of the direct product of two groups, is generalized to describing subgroups of a direct product A1 × A2 × · · · × An of a finite number of groups. Other possible generalizations are discussed and applications characterizing several types of subgroups are given. Most of these applications are straightforward, while somewhat deeper applications occur in the case of profinite groups, cyclic groups, and the Sylow p-subgroups (including infinite groups that are virtual p-groups).

scholarly journals THE LOWER RANK OF DIRECT PRODUCTS OF HEREDITARILY JUST INFINITE GROUPS

2017 ◽  
Vol 60 (1) ◽  
pp. 225-230
Author(s):  
BENJAMIN KLOPSCH ◽  
MATTEO VANNACCI
Keyword(s):  
Direct Product ◽  
Direct Products ◽  
Profinite Groups ◽  
Infinite Groups ◽  
Lower Rank

AbstractWe determine the lower rank of the direct product of finitely many hereditarily just infinite profinite groups of finite lower rank.

A Direct Product Theorem for Two-Party Bounded-Round Public-Coin Communication Complexity

Algorithmica ◽  
2015 ◽  
Vol 76 (3) ◽  
pp. 720-748 ◽  
Author(s):  
Rahul Jain ◽  
Attila Pereszlényi ◽  
Penghui Yao
Keyword(s):  
Direct Product ◽  
Communication Complexity ◽  
Product Theorem
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