Classification of the prime graphs of Sz(8)-, Sz(32)-, and PSL(2, 2 ⁵ )-solvable groups

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The classification of prime graphs for groups whose noncyclic composition factors are isomorphic to a single nonabelian simple group is completed for the previously unsolved cases of Sz(8), Sz(32), and PSL(2, 2^5). Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Thomas Michael Keller; Zachary Martin; Alexa Renner; Gabriel Roca; Eric Yu

doi:10.1515/jgth-2025-0099

July 14, 2026Journal of Group Theory

Classification of the prime graphs of Sz(8)-, Sz(32)-, and PSL(2, 2 ⁵ )-solvable groups

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Key Points

This study aims to complete the classification of prime graphs for specific solvable groups.
Analyzed prime graphs where vertices represent primes dividing the order of the group.
Examined connections between vertices based on elements of specific orders within the groups.
Focused on groups defined as Sz(8), Sz(32), and PSL(2,2^5).
Completed classification for Sz(32) with a comprehensive graph representation.
Established connectivity properties for Sz(8) and PSL(2,2^5).
Confirmed the complexity of prime graphs in these solvable structures.

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Implication

Study classifies prime graphs in solvable groups, suggesting new insights on complex structures.

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Cite This Study

Keller et al. (2026) studied this question.

synapsesocial.com/papers/6a58763f2b46c88ba9ad1dd9 https://doi.org/10.1515/jgth-2025-0099

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Classification of the prime graphs of Sz(8)-, Sz(32)-, and PSL(2, 2 ⁵ )-solvable groups

Key Points

No abstract yet

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Implication

Discussion

Cite This Study

Classification of the prime graphs of Sz(8)-, Sz(32)-, and PSL(2, 2 ⁵ )-solvable groups

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

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