Non-isomorphic 2-groups with isomorphic modular group algebras

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

Suciu’s ribbon 2-knots with isomorphic group

Suciu constructed infinitely many ribbon 2-knots in [Formula: see text] whose knot groups are isomorphic to the trefoil knot group. They are distinguished by the second homotopy groups. We classify these knots by using [Formula: see text]-representations of the fundamental groups of the 2-fold branched covering spaces.

POSITIVE PERMUTATION BRAIDS AND PERMUTATION INVERSIONS WITH SOME APPLICATIONS

In this paper we constructed an isomorphic group of binary matrices to a finite symmetric group. Our method is based on the inversion of permutations. Using this embedding we find an algorithm for writing down a standard braid word representation for each positive permutation braid. Also an algorithm for writing basis of Hecke algebra Hn+1 from such basis of Hn is given.