Maria Silvia Lucido (22 April 1963 – 4 March 2008) was an Italian mathematician specializing in

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

, and a researcher in mathematics at the University of Udine.

Life, education and career

Lucido was originally from

Vicenza Vicenza ( , ; ) is a city in northeastern Italy. It is in the Veneto region at the northern base of the ''Monte Berico'', where it straddles the Bacchiglione River. Vicenza is approximately west of Venice and east of Milan. Vicenza is a thr ...

, where she was born on 22 April 1963. After working for a bank and a travel agency, she entered mathematical study at the

University of Padua The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from ...

in 1986, graduating in 1991. Already as an undergraduate she began research into the theory of finite groups, and wrote an undergraduate thesis on the subject under the supervision of Franco Napolitani. She completed a Ph.D. at Padua in 1996 with the dissertation ''Il Prime Graph dei gruppi finiti'' 'the prime graphs of finite groups'' supervised by Napolitani and co-advised by Carlo Casolo. After postdoctoral research at the University of Padua and as a Fulbright scholar at Michigan State University, she obtained a permanent position as a researcher at the University of Udine in 1999. She was killed in an automobile accident on March 4, 2008, survived by her husband and two sons.

Research

Lucido was particularly known for her research on prime graphs of finite groups. These are

undirected graph In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' ve ...

s that have a vertex for each prime factor of the

order of a group In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is ''infinite''. The ''order'' of an element of a group (also called period length or period) is the order of the subg ...

, and that have an edge

pq

whenever the given group has an element of order

pq

. Her work in this area included *Proving that the connected components of these graphs have

diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...

at most five, and at most three for

solvable group In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminate ...

s. *Proving that, when the prime graph is a

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...

, it has at most eight vertices, and at most four for solvable groups. *Characterizing the

finite simple group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...

s for which all components of the prime graphs are

cliques A clique ( AusE, CanE, or ), in the social sciences, is a group of individuals who interact with one another and share similar interests. Interacting with cliques is part of normative social development regardless of gender, ethnicity, or popular ...

. Lucido founded a series of annual summer schools on the theory of finite groups, held in Venice and sponsored by the University of Udine, beginning in 2004. After her death, the three subsequent offerings of the summer schools in 2010, 2011, and 2013 were dedicated in her honor.

References

{{DEFAULTSORT:Lucido, Maria Silvia 1963 births 2008 deaths Italian mathematicians Italian women mathematicians Group theorists University of Padua alumni