also contributed to geometry, problem solving, and the history of mathematics.
In algebra, I have concentrated on two main areas-commutativity of algebraic systems, and automorphisms of finite groups. I have written about twenty-five original research papers in these areas and my work has been developed and extended by several of my students and by many international research workers.
BIOGRAPHY
Research Interests
My main research area has been algebra,especially finite groups and rings, but I havealso contributed to geometry, problem solving, and the history of mathematics.
In algebra, I have concentrated on two main areas-commutativity of algebraic systems, and automorphisms of finite groups. I have written about twenty-five original research papers in these areas and my work has been developed and extended by several of my students and by many international research workers.
I have written the first full-length biography of George Boole which is now regarded
as the seminal work in this area. I teach one of the few courses on the history of mathematics in these Islands and my students and I have produced a large amount of research on the life and work of many eminent Irish mathematicians .
Publications
Books
| Year | Publication | |
|---|---|---|
| (1993) | COMIC SECTIONS. D. MacHale; (1993) COMIC SECTIONS. Dublin: Boole Press. [Details] | |
| (1985) | GEORGE BOOLE ¿HIS LIFE AND WORK. D. MacHale; (1985) GEORGE BOOLE ¿HIS LIFE AND WORK. Dublin: Boole Press. [Details] |
Peer Reviewed Journals
| Year | Publication | |
|---|---|---|
| (2008) | 'ON THE SUM OF THE CHARACTER DEGREES OF A FINITE GROUP' With R.Heffernan; (2008) 'ON THE SUM OF THE CHARACTER DEGREES OF A FINITE GROUP' [Details] | |
| (2008) | 'THE DISTANCE FROM A POINT TO A LINE' D. MacHale; (2008) 'THE DISTANCE FROM A POINT TO A LINE' [Details] | |
| (2008) | 'THE WELL¿ORDERING PRINCIPLE FOR N' D. MacHale; (2008) 'THE WELL¿ORDERING PRINCIPLE FOR N' [Details] | |
| (2008) | 'INTEGRATION WITHOUT TEARS' D. MacHale; (2008) 'INTEGRATION WITHOUT TEARS' [Details] | |
| (2007) | 'POSITIVE SOLUTIONS OF MORDELL¿S EQUATION' D. MacHale; (2007) 'POSITIVE SOLUTIONS OF MORDELL¿S EQUATION' [Details] | |
| (2006) | 'SOME SUPERSOLUBILITY CONDITIONS FOR FINITE GROUPS' With F.Barry and A Ni She; (2006) 'SOME SUPERSOLUBILITY CONDITIONS FOR FINITE GROUPS' [Details] | |
| (2005) | 'ON A PARTICULAR DIOPHANTINE EQUATION' D. MacHale; (2005) 'ON A PARTICULAR DIOPHANTINE EQUATION' [Details] | |
| (2004) | 'FINITE GROUPS WITH FEW AUTOMORPHISMS' D. MacHale With R.Sheehy; (2004) 'FINITE GROUPS WITH FEW AUTOMORPHISMS' [Details] | |
| (2003) | 'SOME IMPROVED DISSECTIONS OF SQUARES' D. MacHale With J.Kingston; (2003) 'SOME IMPROVED DISSECTIONS OF SQUARES' [Details] | |
| (2001) | 'DISSECTING SQUARES' D, MacHale With J.Kingston; (2001) 'DISSECTING SQUARES' [Details] | |
| (2001) | '(a+b)^(-1) = a^(-1) + b^(-1) REVISITED' D. MacHale; (2001) '(a+b)^(-1) = a^(-1) + b^(-1) REVISITED' [Details] | |
| (2000) | 'DIOPHANTINE BOXES' D. MacHale; (2000) 'DIOPHANTINE BOXES' [Details] | |
| (1997) | 'THE SUBGROUP GENERATED BY THE SQUARES' D. MacHale; (1997) 'THE SUBGROUP GENERATED BY THE SQUARES' [Details] | |
| (1997) | 'LOWER CENTRAL SERIES OF GROUPS WITH SMALL UPPER CENTRAL FACTORS' D, MacHale With Burns et al; (1997) 'LOWER CENTRAL SERIES OF GROUPS WITH SMALL UPPER CENTRAL FACTORS' [Details] | |
| (1995) | 'FINITE GROUPS WITH ODD ORDER AUTOMORPHISM GROUPS' D. MacHale; (1995) 'FINITE GROUPS WITH ODD ORDER AUTOMORPHISM GROUPS' [Details] | |
| (1994) | 'COMMUTATOR SUBGROUPS OF FINITE GROUPS' D. MacHale, O¿Murchu and Wiegold; (1994) 'COMMUTATOR SUBGROUPS OF FINITE GROUPS' [Details] | |
| (1994) | 'FINITE GROUPS WHOSE AUTOMORPHISM GROUPS ARE 2-GROUPS' D. MacHale; (1994) 'FINITE GROUPS WHOSE AUTOMORPHISM GROUPS ARE 2-GROUPS' [Details] | |
| (1994) | 'FINITE GROUPS WHOSE AUTOMORPHISM GROUPS ARE 2¿GROUPS' D. MacHale, Flynn et al; (1994) 'FINITE GROUPS WHOSE AUTOMORPHISM GROUPS ARE 2¿GROUPS' [Details] | |
| (1992) | 'POLYNOMIALS THAT FORCE A RING TO BE COMMUTATIVE' D. MacHale T.J.Laffey; (1992) 'POLYNOMIALS THAT FORCE A RING TO BE COMMUTATIVE' [Details] | |
| (1991) | 'DETERMINING ALL FINITE GROUPS WHOSE AUTOMORPHISM IS A P¿GROUP' D. MacHale J.Flynn; (1991) 'DETERMINING ALL FINITE GROUPS WHOSE AUTOMORPHISM IS A P¿GROUP' [Details] | |
| (1986) | 'CHARACTERISTIC ELEMENTS IN GROUPS' D. MacHale; (1986) 'CHARACTERISTIC ELEMENTS IN GROUPS' [Details] | |
| (1983) | 'RINGS THAT ARE NEARLY BOOLEAN III' D. MacHale; (1983) 'RINGS THAT ARE NEARLY BOOLEAN III' [Details] | |
| (1983) | 'SOME FINITE GROUPS WHICH ARE RARELY AUTOMORPHISM GROUPS II' D. MacHale; (1983) 'SOME FINITE GROUPS WHICH ARE RARELY AUTOMORPHISM GROUPS II' [Details] | |
| (1982) | 'IDEMPOTENTS IN FINITE RINGS' D. MacHale; (1982) 'IDEMPOTENTS IN FINITE RINGS' [Details] | |
| (1982) | 'CONSTRUCTING INTEGER ANGLES' D. MacHale; (1982) 'CONSTRUCTING INTEGER ANGLES' [Details] | |
| (1981) | 'SOME FINITE GROUPS WHICH ARE RARELY AUTOMORPHISM GROUPS I' D. MacHale D.Flannery; (1981) 'SOME FINITE GROUPS WHICH ARE RARELY AUTOMORPHISM GROUPS I' [Details] | |
| (1980) | 'RINGS THAT ARE NEARLY BOOLEAN' D. MacHale; (1980) 'RINGS THAT ARE NEARLY BOOLEAN' [Details] | |
| (1976) | 'MINIMUM COUNTEREXAMPLES IN GROUP THEORY' D. MacHale; (1976) 'MINIMUM COUNTEREXAMPLES IN GROUP THEORY' [Details] | |
| (1974) | 'POWER MAPPINGS AND GROUP MORPHISMS' D. MacHale; (1974) 'POWER MAPPINGS AND GROUP MORPHISMS' [Details] |
Other Journals
| Year | Publication | |
|---|---|---|
| (1998) | 'TOTALLY NON¿COMMUTATIVE SYSTEMS' D. MacHale; (1998) 'TOTALLY NON¿COMMUTATIVE SYSTEMS' Math Gazette, . [Details] | |
| (1998) | 'TWO¿GROUPS IN WHICH AN AUTOMORPHISM INVERTS PRECISELY HALF THE ELEMENTS' D. MacHale With P.Hegarty; (1998) 'TWO¿GROUPS IN WHICH AN AUTOMORPHISM INVERTS PRECISELY HALF THE ELEMENTS' Bull.London Math Soc, 30 (2) :129-135. [Details] | |
| (1997) | 'VANISHING COFFEE MORNINGS AND IRISH ELECTIONS' D. MacHale; (1997) 'VANISHING COFFEE MORNINGS AND IRISH ELECTIONS' Math Gazette, . [Details] | |
| (1996) | '`WHEN IS A FINITE RING A FIELD?' D. MacHale; (1996) '`WHEN IS A FINITE RING A FIELD?' Irish Math Society Bull, (37) :35-38. [Details] | |
| (1995) | 'PRODUCTS OF GROUP COMMUTATORS' D. Machale; (1995) 'PRODUCTS OF GROUP COMMUTATORS' Irish Math Soc, . [Details] | |
| (1994) | 'EPIMORPHISMS ACTING ON BURNSIDE' D. MacHale; (1994) 'EPIMORPHISMS ACTING ON BURNSIDE' Irish Math. Soc. Bull, . [Details] | |
| (1993) | 'COMMUTATOR SUBGROUPS OF GROUPS WITH SMALL CENTRAL FACTOR GROUPS' D. Machale, P.O¿Murchu; (1993) 'COMMUTATOR SUBGROUPS OF GROUPS WITH SMALL CENTRAL FACTOR GROUPS' Proc.Roy.Ir. Acad, . [Details] | |
| (1992) | '0 = x¿x' D. MacHale; (1992) '0 = x¿x' Math Gazette, . [Details] | |
| (1992) | 'HOW EASY IS A GOLF PUTT?' D. MacHale; (1992) 'HOW EASY IS A GOLF PUTT?' Math Gazette, . [Details] | |
| (1991) | 'MY FAVOURITE POLYNOMIAL' D. MacHale; (1991) 'MY FAVOURITE POLYNOMIAL' Math Gazette, . [Details] | |
| (1990) | 'PROBABILITY IN FINITE SEMIGROUPS' D. MacHale; (1990) 'PROBABILITY IN FINITE SEMIGROUPS' Irish Math Soc.Bull, . [Details] | |
| (1990) | 'A REMARK ON BOOLEAN RINGS' D. MacHale; (1990) 'A REMARK ON BOOLEAN RINGS' Math.Mag, . [Details] | |
| (1989) | 'THE 3¿4¿5 TRIANGLE AGAIN' Math Gazette; (1989) 'THE 3¿4¿5 TRIANGLE AGAIN' Math Gazette, . [Details] | |
| (1989) | 'ELEMENTS' D. MacHale M.Deaconescu; (1989) 'ELEMENTS' J.Austral.Math. Soc, . [Details] | |
| (1988) | 'WEDDERBURN¿S THEOREM REVISITED (AGAIN)' D. MacHale; (1988) 'WEDDERBURN¿S THEOREM REVISITED (AGAIN)' Irish Math Soc.Bull, . [Details] | |
| (1987) | 'AN ANTICOMMUTATIVITY CONSEQUENCE OF A RING COMMUTATIVITY THEOREM OF HERSTEIN' D. MacHale; (1987) 'AN ANTICOMMUTATIVITY CONSEQUENCE OF A RING COMMUTATIVITY THEOREM OF HERSTEIN' American Mathematical Monthly, . [Details] | |
| (1987) | 'OPERATIONS DISTRIBUTIVE OVER EACH OTHER' K.Fraher, D. Machale; (1987) 'OPERATIONS DISTRIBUTIVE OVER EACH OTHER' Math. Gazette, . [Details] | |
| (1987) | 'NONCOMMUTATIVE ANTICOMMUTATIVE RINGS' D. MacHale S.Buckley; (1987) 'NONCOMMUTATIVE ANTICOMMUTATIVE RINGS' Irish Math Soc Bull, . [Details] | |
| (1986) | 'AUTOMORPHISM ORBITS IN FINITE GROUPS' T.J.Laffey, D. MacHale; (1986) 'AUTOMORPHISM ORBITS IN FINITE GROUPS' J.Austral. Math. Soc, . [Details] | |
| (1981) | 'MINIMUM COUNTEREXAMPLES IN GROUP THEORY' D. MacHale; (1981) 'MINIMUM COUNTEREXAMPLES IN GROUP THEORY' Math.Mag, . [Details] | |
| (1976) | 'COMMUTATIVITY IN FINITE RINGS' D. MacHale; (1976) 'COMMUTATIVITY IN FINITE RINGS' American Mathematical Monthly, . [Details] | |
| (1973) | 'GROUPS OF ODD ORDER WITH AN AUTOMORPHISM INVERTING MANY ELEMENTS' H.Liebeck, D. MacHale; (1973) 'GROUPS OF ODD ORDER WITH AN AUTOMORPHISM INVERTING MANY ELEMENTS' J.London Math Soc, . [Details] | |
| (1972) | 'GROUPS WITH AUTOMORPHISMS INVERTING MOST ELEMENTS' H. Liebeck, D. Machale; (1972) 'GROUPS WITH AUTOMORPHISMS INVERTING MOST ELEMENTS' Math. Z, . [Details] |
Conference Contributions
| Year | Publication | |
|---|---|---|
| (2005) | International Conference on Group Theory, D.MacHale; (2005) Supersolubility in Finite Groups. [Oral Presentation], International Conference on Group Theory, St Andrews University , 08-AUG-05 - 08-AUG-08 |
Professional Activities
Honours and Awards
| Year | Title | Awarding Body | |
|---|---|---|---|
| 2004 | Teaching Award for Course on Problem Solving (With D.Hurley and T.Carroll) | UCC | |
| 2005 | Award for best paper on Geometric Dissections in Mathematical Gazette (With Joe Kingston) | Mathematical Association |
Employment
| Employer | Position | From / To | |
|---|---|---|---|
| Dept of Mathemathics, UCC | Associate Professor | / | |
| UCC | Statutory Lecturer | 05-JUN-92 / 07-JUN-96 | |
| UCC | College Lecturer | / |
Education
| Year | Instituion | Qualification | Subject | |
|---|---|---|---|---|
| 1968 | UCG | BSC | Mathemathics | |
| 1968 | UCG | MSc | Mathemathtics | |
| 1972 | University of Keele | PHD | Maths | |
| 1998 | UCC | Diploma | Geology |
Other Activities
| Description | |
|---|---|
Visits Abroad 2004 St. Andrew's University To deliver a course of lectures on | |
Research Talks 2005 Automorphisms of Finite groups NUIG May 15 2006 Some Supersolubility Conditions for Finite Groups NUIG May 16 2008 On the Sum of Character Degrees of a Finite Group NUIG May 14 | |
Expert Assignments 2004 External Examiner for Ph.D Thesis in Group Theory. Oxford University 2005 Internal Examiner for Ph.D Thesis in Group Theory UCC |
