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Comp."],"abstract":"<p>\n                    In this work we develop a method to parametrize the set\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper I normal r normal r left-parenthesis upper U right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"normal\">I<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">r<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">r<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>U<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathrm {Irr}(U)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of irreducible characters of a Sylow\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -subgroup\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U\">\n                        <mml:semantics>\n                          <mml:mi>U<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">U<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of a finite Chevalley group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G left-parenthesis p Superscript f Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mi>f<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">G(p^f)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    which is valid for arbitrary primes\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , in particular, when\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is a very bad prime for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G\">\n                        <mml:semantics>\n                          <mml:mi>G<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">G<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . As an application, we parametrize\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper I normal r normal r left-parenthesis upper U right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"normal\">I<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">r<\/mml:mi>\n                              <mml:mi mathvariant=\"normal\">r<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>U<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathrm {Irr}(U)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    when\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper G equals normal upper F 4 left-parenthesis 2 Superscript f Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>G<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">F<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mn>4<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mi>f<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">G=\\mathrm {F}_4(2^f)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/mcom\/3488","type":"journal-article","created":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T12:44:11Z","timestamp":1570625051000},"page":"1501-1524","source":"Crossref","is-referenced-by-count":0,"title":["On the characters of Sylow \ud835\udc5d-subgroups of finite Chevalley groups \ud835\udc3a(\ud835\udc5d^{\ud835\udc53}) for arbitrary primes"],"prefix":"10.1090","volume":"89","author":[{"given":"Tung","family":"Le","sequence":"first","affiliation":[]},{"given":"Kay","family":"Magaard","sequence":"additional","affiliation":[]},{"given":"Alessandro","family":"Paolini","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2019,11,19]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics, Vol. 28","volume-title":"Simple groups of Lie type","author":"Carter, Roger W.","year":"1972"},{"key":"2","series-title":"Pure and Applied Mathematics (New York)","isbn-type":"print","volume-title":"Finite groups of Lie type","author":"Carter, Roger W.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0471905542"},{"key":"3","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139172417","volume-title":"Representations of Finite Groups of {L}ie Type","volume":"21","author":"Digne, F.","year":"1991"},{"issue":"2","key":"4","doi-asserted-by":"crossref","first-page":"325","DOI":"10.4099\/math1924.12.325","article-title":"The characters of G\u2082(2\u207f)","volume":"12","author":"Enomoto, H.","year":"1986","journal-title":"Japan. 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