score:3

Accepted answer
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>
<div id="app">
</div>

score:2

const obj = {
  team1 : {
    author92 : "John" , 
    author43 : "Smith" 
  },
  team2 : {
    author33 : "Dolly", 
    author23 : "Mark" 
  },
};

class App extends React.Component {
  render() {
    const teams = [];
    let teamNum = 1;
    let authorsStartWith = 1;

    Object.keys(obj).forEach(key => {
      teams.push({
        team: obj[key],
        teamNum,
        authorsStartWith,
      });
      teamNum += 1;
      authorsStartWith += Object.keys(obj[key]).length;
    });

    return (
      <div>
        {
          teams.map(team =>
            <Team
              team={team.team}
              teamNum={team.teamNum}
              authorsStartWith={team.authorsStartWith}
              key={team.teamNum}
            />
          )
        }
      </div>
    )
  }
}


class Team extends React.Component {
  constructor(props) {
    super(props);
  }

  render() {
    return (
      <div>
        <p>Group {this.props.teamNum}</p>
        <ol start={this.props.authorsStartWith}>
          {
            Object.values(this.props.team)
              .map(authorName =>
                    <li
                    key={`${this.props.groupName}_${authorName}`}
                  >
                    {authorName}
                  </li>)
          }
        </ol>
      </div>
    );
  }
}

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