On the quadratic functional equation on groups

Peter de Place Friis; Henrik Stetkær

On the quadratic functional equation on groups

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Abstract

^{We study the solutions f: G→H of the quadratic functional equation on G, where G and H are groups, H abelian. We show that any solution f is a function on the quotient group [G,[G,G]]. By help of this we find sufficient conditions on G for all solutions to satisfy Kannappan's condition. We use this to derive explicit formulas for the solutions on various groups like, e.g. the (ax+b)-group and GL(n,R).}

Original language	English
Journal	Publ. Math. Debrecen
Volume	69
Issue	1-2
Pages (from-to)	65-93
Publication status	Published - 2006

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title = "On the quadratic functional equation on groups",

abstract = "We study the solutions f: G→H of the quadratic functional equation on G, where G and H are groups, H abelian. We show that any solution f is a function on the quotient group [G,[G,G]]. By help of this we find sufficient conditions on G for all solutions to satisfy Kannappan's condition. We use this to derive explicit formulas for the solutions on various groups like, e.g. the (ax+b)-group and GL(n,R).",

author = "Friis, {Peter de Place} and Henrik Stetk{\ae}r",

year = "2006",

language = "English",

volume = "69",

pages = "65--93",

journal = "Publ. Math. Debrecen",

number = "1-2",

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TY - JOUR

T1 - On the quadratic functional equation on groups

AU - Friis, Peter de Place

AU - Stetkær, Henrik

PY - 2006

Y1 - 2006

N2 - We study the solutions f: G→H of the quadratic functional equation on G, where G and H are groups, H abelian. We show that any solution f is a function on the quotient group [G,[G,G]]. By help of this we find sufficient conditions on G for all solutions to satisfy Kannappan's condition. We use this to derive explicit formulas for the solutions on various groups like, e.g. the (ax+b)-group and GL(n,R).

AB - We study the solutions f: G→H of the quadratic functional equation on G, where G and H are groups, H abelian. We show that any solution f is a function on the quotient group [G,[G,G]]. By help of this we find sufficient conditions on G for all solutions to satisfy Kannappan's condition. We use this to derive explicit formulas for the solutions on various groups like, e.g. the (ax+b)-group and GL(n,R).

M3 - Journal article

VL - 69

SP - 65

EP - 93

JO - Publ. Math. Debrecen

JF - Publ. Math. Debrecen

IS - 1-2

ER -

On the quadratic functional equation on groups

Abstract

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