SCHUR'S EXPONENT CONJECTURE | COUNTEREXAMPLES OF EXPONENT 5 AND EXPONENT 9

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VAUGHAN-LEE MICHAEL

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2021 | Volume:10 | Issue:4 Page(s): 167-173

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Title

SCHUR'S EXPONENT CONJECTURE | COUNTEREXAMPLES OF EXPONENT 5 AND EXPONENT 9

Author(s)

VAUGHAN-LEE MICHAEL | Issue Writer Certificate

Keywords

Finite group

Sylow subgroup

abnormal subgroup

seminormal subgroup

Abstract

1. Introduction: There is a long-standing conjecture attributed to I. Schur that if G is a , nite group with Schur multiplier M(G) then the exponent of M(G) divides the exponent of G. It is easy to show that this is true for groups G of exponent 2 or exponent 3, but it has been known since 1974 that the conjecture fails for exponent 4. Bayes, Kautsky and Wamsley [1] give an example of a group G of order 2 with exponent 4, where M(G) has exponent 8. (Bayes, Kautsky and Wamsley are heros of the early days of computing with , nite p-groups. ) However the truth or otherwise of this conjecture has remained open up till now for groups of odd exponent, and in particular it has remained open for groups of exponent 5 and exponent 9. For a survey article on Schur's conjecture see Thomas [6]...

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APA: Copy

VAUGHAN-LEE, MICHAEL. (2021). SCHUR'S EXPONENT CONJECTURE | COUNTEREXAMPLES OF EXPONENT 5 AND EXPONENT 9. INTERNATIONAL JOURNAL OF GROUP THEORY, 10(4), 167-173. SID. https://sid.ir/paper/1004166/en

Vancouver: Copy

VAUGHAN-LEE MICHAEL. SCHUR'S EXPONENT CONJECTURE | COUNTEREXAMPLES OF EXPONENT 5 AND EXPONENT 9. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2021;10(4):167-173. Available from: https://sid.ir/paper/1004166/en

IEEE: Copy

MICHAEL VAUGHAN-LEE, “SCHUR'S EXPONENT CONJECTURE | COUNTEREXAMPLES OF EXPONENT 5 AND EXPONENT 9,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 10, no. 4, pp. 167–173, 2021, [Online]. Available: https://sid.ir/paper/1004166/en

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