Bicrossed products for finite groups

Abstract

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.

Final version: to appear in Algebras and Representation Theory

References in corpus (1)

• On the classification of twisting maps between $K^n$ and $K^m$

Cited by in corpus (6)

• Extending structures I: the level of groups
• Classifying bicrossed products of Hopf algebras
• Zappa-Szép products of Garside monoids
• Hopf Algebras which Factorize through the Taft Algebra $T_{m^2}(q)$ and the Group Hopf Algebra $K[C_n]$
• Deterministic Algorithms for the Hidden Subgroup Problem
• Bicrossed products with the Taft algebra