Groups with Identical k-Profiles
TLDR
It is shown that for 1 k-generated subgroups, the multiset of isomorphism types of $k$- generated subgroups does not determine a group of order at most $n$.Abstract:
We show that for $1 \le k \le \sqrt{2\log_3 n}-(5/2)$, the multiset of isomorphism types of $k$-generated subgroups does not determine a group of order at most $n$. This answers a question raised by Tim Gowers in connection with the Group Isomorphism problem.read more
Citations
More filters
Posted Content
Graph Isomorphism in Quasipolynomial Time
TL;DR: The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques and shows that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioned.
Proceedings ArticleDOI
Graph isomorphism in quasipolynomial time [extended abstract]
TL;DR: This work builds on Luks’s framework and attack the obstructions to efficient Luks recurrence via an interplay between local and global symmetry, and constructs group theoretic “local certificates” to certify the presence or absence of local symmetry.
Proceedings ArticleDOI
On the Weisfeiler-Leman Dimension of Finite Groups
TL;DR: The results indicate that the Weisfeiler-Leman algorithm can be more effective in distinguishing groups than in distinguishing graphs based on similar combinatorial constructions.
Journal ArticleDOI
The threshold for subgroup profiles to agree is $\Omega(\log n)$
TL;DR: For primes $p,e>2, there are at least polylogarithmic-time isomorphism tests for general finite groups of order $p 2e+2, where ρ is the number of proper subgroups.
Posted Content
On the Weisfeiler-Leman Dimension of Finite Groups
TL;DR: In this paper, the Weisfeiler-Leman algorithm is used to construct groups with high Weisberg dimension 3, and the results indicate that the algorithm can be more effective in distinguishing groups than in distinguishing graphs.
References
More filters
Posted Content
Graph Isomorphism in Quasipolynomial Time
TL;DR: The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques and shows that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioned.
Posted Content
Group Isomorphism with Fixed Subnormal Chains.
TL;DR: This paper focuses here on the fixed-composition-series subproblem and exhibits a polynomial-time algorithm that is valid for general groups and will construct canonical forms within the same time bound.
Related Papers (5)
Isomorphism of Modular Group Algebras of p-Mixed Abelian Groups
Upper Bounds for the Number of Conjugacy Classes of a Finite Group
Martin W. Liebeck,László Pyber +1 more